A whole optimization method considering adjacent line element relationship of railway plane line shape

Abstract

The application discloses a kind of overall optimization method considering adjacent line element relationship of railway plane alignment, belong to the application category of precision engineering surveying technique in rail transit field.It is segmented to the railway line to be adjusted;Function expression of the measuring point measurement coordinate corresponding to the line segment is established;Error equation of the measured coordinate corresponding to the line segment is listed;Length constraint and / or slope and azimuth constraint of adjacent line element relationship of railway plane alignment are established, and the error equation of the estimated parameter in constraint is obtained by total differentiation;The error equation of the measured coordinate corresponding to the line segment, and the error equation of length constraint and / or slope and azimuth constraint are solved and obtained by simultaneous equation, and the optimized railway line parameter and distance amount are obtained.The present application can solve the misalignment phenomenon between different line shapes caused by single line shape fitting and recombination, and improve the overall smoothness of the line.

Description

Technical Field

[0001] This invention relates to the field of precision engineering measurement technology for railway tracks, and in particular to an overall optimization method that takes into account the relationship between adjacent line elements of the railway plane alignment. Background Technology

[0002] The smoothness of railway lines is crucial for high-speed train operation and safe maintenance. During the maintenance of existing tracks, the railway alignment parameters form the basis for track inspection and maintenance by railway engineering departments, and are typically based on the original design parameters. After a railway opens for operation, the rails are affected by wheel-rail forces, causing significant changes in their geometry. Adjusting the track geometry based solely on the original design parameters would significantly increase maintenance workload and costs. Therefore, it is necessary to optimize and control the smoothness of the track alignment based on measured track conditions. This ensures that the optimized alignment parameters meet the requirements of the track design specifications while minimizing the workload of track adjustments. Currently, track alignment optimization methods are mainly based on the idea of ​​fitting and recombining single alignment types. This lacks strong correlation between different alignment functions, relying solely on simple parameters such as transition curves and radii to address the weak correlation between different alignment functions. This leads to misalignment between optimized alignment types, severely impacting the smoothness of the optimized track. Summary of the Invention

[0003] To address the aforementioned problems, this invention aims to provide a holistic optimization method that considers the relationships between adjacent elements of railway horizontal alignment. By using the strong correlation between different alignment functions as constraints, and through the overall optimization of different alignment function models, it solves the misalignment problem between different alignments that exists after optimization using conventional line optimization methods. While considering the workload, it further improves the smoothness of the optimized line, providing an optimal solution for railway line operation and maintenance.

[0004] The technical solution of the present invention is as follows:

[0005] A holistic optimization method that takes into account the relationship between adjacent elements of railway horizontal alignment includes the following steps:

[0006] S1: Divide the railway line to be adjusted into sections;

[0007] S2: The measured coordinates of a straight line segment in the measurement coordinate system are expressed by a straight line function, and the measured coordinates of a transition curve segment / circular curve segment in the measurement coordinate system are expressed as a function of independent coordinates in the tangent coordinate system;

[0008] S3: Linearize the measured coordinate function and list the error equations for the measured coordinates of the corresponding line segments;

[0009] S4: Establish length constraints and / or slope and azimuth constraints for the relationship between adjacent line elements of the railway horizontal alignment. The length constraint is an equivalent constraint relationship in which the theoretical value of the measured coordinate difference between the starting straight-to-gradient point and the ending round-to-round point of the transition curve segment / the starting straight-to-gradient point and the ending round-to-gradient point is converted into the tangent coordinates of the round-to-round point / the round-to-gradient point. The slope and azimuth constraints are equivalent constraint relationships in which the slope of the straight line segment is converted into the azimuth of the horizontal axis of the tangent coordinate system of the adjacent transition curve segment.

[0010] S5: Take the total differential of the parameters to be estimated in the length constraint and / or slope and azimuth constraint to obtain the error equation;

[0011] S6: Solve the error equations of the measured coordinates, length constraint error equations, and / or slope and azimuth constraint error equations on the line segment to be adjusted, and obtain the optimized railway line and clearance.

[0012] Preferably, in step S1, the railway line includes two or more of the following adjacent segments: a straight section before the railway line, a first transition curve section, a circular curve section, a second transition curve section, and a straight section after the railway line.

[0013] Preferably, in step S2, the linear function includes measured coordinates, slope, and intercept. The tangent coordinate system is a rectangular coordinate system with the straight-to-gradient point / gradual-to-straight point of the railway line as the origin, the tangent pointing in the direction of the corresponding intersection point as the x-axis, and the direction perpendicular to the tangent and pointing in the direction of the circle center as the y-axis. The independent coordinates in the tangent coordinate system are expressed by the transition curve equation / circular curve equation.

[0014] Preferably, the transition curve equation / circular curve equation is the transition curve / circular curve equation of the curve determined by the tangent offset method.

[0015] Preferably, the equation of the transition curve includes the length of the transition curve, the radius of the circular curve, and the curve length from the measuring point on the transition curve to the straight-to-transition point / transition-to-straight point. The equation of the circular curve includes the length of the transition curve, the radius of the circular curve, the curve length from the measuring point on the circular curve to the straight-to-transition point / transition-to-straight point, the tangent angle of the transition curve, the perpendicular distance, and the inward displacement of the circular curve.

[0016] As an optimization, the independent coordinates in the tangent coordinate system are tangent coordinates.

[0017] Preferably, in step S3, if the corresponding line segment includes a front clamping straight line segment, then the error equation for the measured coordinates of the front clamping straight line segment is listed; if it includes a rear clamping straight line segment, then the error equation for the measured coordinates of the rear clamping straight line segment is listed; if it includes a first transition curve segment, then the error equation for the measured coordinates of the first transition curve segment is listed; if it includes a circular curve segment, then the error equation for the measured coordinates of the circular curve segment is listed; if it includes a second transition curve segment, then the error equation for the measured coordinates of the second transition curve segment is listed.

[0018] Preferably, the parameters to be estimated in the error equation of the measured coordinates of the first clamping straight line segment include one or more of the following: the slope of the first clamping straight line, the intercept of the first clamping straight line, and coordinates. The parameters to be estimated in the error equation of the measured coordinates of the second clamping straight line segment include one or more of the following: the slope of the second clamping straight line, the intercept of the second clamping straight line, and coordinates. The coordinates are one or more of the north coordinates and east coordinates of the measuring point. The parameters to be estimated in the error equation of the measured coordinates of the first transition curve segment include the azimuth of the tangent at the transition point, the measured coordinates of the transition point, the radius of the circular curve, the length of the first transition curve, and the distance from the measuring point on the first transition curve segment to the transition point. The parameters to be estimated in the error equation of the measured coordinates of the second transition curve segment include one or more of the following: the azimuth of the tangent at the transition point, the measured coordinates of the transition point, the radius of the circular curve, the length of the second transition curve, and the curve length from the measured point on the second transition curve segment to the transition point. The parameters to be estimated in the error equation of the measured coordinates of the circular curve segment include one or more of the following: the azimuth of the tangent at the transition point / the azimuth of the tangent at the transition point, the radius of the circular curve, the length of the transition curve, the measured coordinates of the transition point / the measured coordinates of the transition point, and the curve length from the measured point on the circular curve segment to the transition point / the curve length from the transition point.

[0019] Preferably, in step S4, the length constraint includes one or more of the length constraint of the first transition curve length and the length constraint of the second transition curve length, the tangent coordinates are coordinates in the tangent coordinate system, and the slope and azimuth constraints include one or more of the relationship between the slope of the front straight line and the azimuth of the tangent at the transition point of the first transition curve segment, and the relationship between the slope of the rear straight line and the azimuth of the tangent at the transition point of the second transition curve segment.

[0020] Preferably, in step S5, the parameters to be estimated for the length constraint include one or more of the parameters to be estimated for the length constraint of the first transition curve segment and the parameters to be estimated for the length constraint of the second transition curve segment. The parameters to be estimated for the length constraint of the first transition curve segment include one or more of the measured coordinates of the straight-to-turn point, the measured coordinates of the transition-to-round point, the azimuth angle of the tangent at the straight-to-turn point, the length of the first transition curve, and the length of the round curve. The parameters to be estimated for the length constraint of the second transition curve segment include one or more of the measured coordinates of the transition-to-straight point, the measured coordinates of the round-to-turn point, the azimuth angle of the tangent at the transition-to-straight point, the length of the second transition curve, and the length of the round curve. The parameters to be estimated for the slope and azimuth constraints include one or more of the following: the relationship between the slope of the preceding clamping line and the azimuth angle of the tangent at the straight-to-straight point of the first transition curve segment; and the relationship between the slope of the following clamping line and the azimuth angle of the tangent at the straight-to-straight point of the second transition curve segment. The parameters to be estimated for the relationship between the slope of the preceding clamping line and the azimuth angle of the tangent at the straight-to-straight point of the first transition curve segment include one or more of the following: the slope of the preceding clamping line and the azimuth angle of the tangent at the straight-to-straight point. The parameters to be estimated for the relationship between the slope of the following clamping line and the azimuth angle of the tangent at the straight-to-straight point of the second transition curve segment include one or more of the following: the slope of the following clamping line and the azimuth angle of the tangent at the straight-to-straight point.

[0021] Preferably, in step S6, the solution method includes one of the following: conventional least squares method, orthogonal least squares method, global / overall least squares method, weighted global / overall least squares method, and constrained global / overall least squares method.

[0022] Compared with the prior art, the present invention has the following advantages:

[0023] This invention uses the strong correlation between different linear functions as constraints, and performs overall optimization and solution on different linear function models and the strong constraints between functions. It can solve the problem that conventional line optimization methods only deal with different linear function models, resulting in misalignment between different lines after optimization. While taking into account the workload, it further improves the smoothness of the optimized line and provides a scientific and accurate optimization control scheme for railway line operation and maintenance. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, 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.

[0025] Figure 1 This is a schematic diagram of the overall scheme flow of an embodiment of the present invention;

[0026] Figure 2 This is a detailed technical solution flowchart of an embodiment of the present invention;

[0027] Figure 3 This is a schematic diagram of the relationship between adjacent line elements in an embodiment of the present invention. Detailed Implementation

[0028] The present invention will be further described below with reference to the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and technical features described in this application can be combined with each other. Unless otherwise defined, the technical or scientific terms used in this invention should be understood in their ordinary sense by those skilled in the art to which this disclosure pertains. The terms "comprising" or "including," and similar terms used in this invention, mean that the element or object preceding the word covers the element or object listed following the word and its equivalents, but does not exclude other elements or objects.

[0029] like Figure 1-3 As shown, a holistic optimization method considering the relationship between adjacent elements of railway horizontal alignment includes the following steps:

[0030] S1: The railway line to be adjusted is divided into segments. The railway line includes two or more of the following adjacent segments: the preceding straight section, the first transition curve section, the circular curve section, the second transition curve section, and the following straight section.

[0031] In specific embodiments, the railway line can be a straight section followed by a first transition curve section, or a first transition curve section followed by a circular curve section, or a circular curve section followed by a second transition curve section, or a second transition curve section followed by a straight section, or a straight section followed by a first transition curve section followed by a circular curve section, or a first transition curve section followed by a circular curve section followed by a second transition curve section, or a circular curve section followed by a second transition curve section and a straight section followed by a straight section, or a straight section followed by a first transition curve section followed by a circular curve section followed by a second transition curve section and a straight section followed by a straight section, or a straight section followed by a first transition curve section followed by a circular curve section followed by a second transition curve section and a straight section followed by a straight section, or a straight section followed by a first transition curve section followed by a circular curve section followed by a second transition curve section and a straight section followed by a straight section.

[0032] In a specific embodiment, the segmentation method is railway horizontal alignment identification segmentation, which includes coarse segmentation and precise segmentation. Coarse segmentation involves determining the location of each measuring point within one of the following segments: the preceding straight section, the first transition curve section, the circular curve section, the second transition curve section, and the following straight section, as well as the positions of the straight-to-transition point, the transition-to-circular point, the circular-to-transition point, and the transition-to-straight point.

[0033] In specific embodiments, coarse segmentation can be achieved using one of the following methods: curvature method, versine method, or slope method. The curvature method can be one of the three-point circle curvature method or the eleven-point curvature method.

[0034] Precise segmentation involves using rigorous adjustment methods to fit the preceding and following straight lines and circular curves to the positions of the measured points within the segments obtained from the coarse segmentation. This determines the positions of four characteristic points: the straight-to-gradient point, the gradual-to-circular point, the circular-to-gradient point, and the gradual-to-straight point. Based on these characteristic point positions, the measured points are then re-divided within their respective segments. This process is repeated until a certain threshold is met. At this point, the characteristic points are stable, and the positions of the measured points within their respective segments are determined.

[0035] In specific embodiments, the rigorous adjustment method is one of the following: conventional least squares method, orthogonal least squares method, overall / total least squares method, weighted overall / total least squares method, and constrained overall / total least squares method.

[0036] In a specific embodiment, the steps for precise segmentation are as follows:

[0037] 1) Use the curvature method, versine method or slope method to roughly segment the plane curve to obtain the approximate location of each feature point.

[0038] 2) Based on the conventional least squares method or the orthogonal least squares method, the line segment is fitted, and the slopes k1 and k3, and the intercepts k2 and k4 of the line segment are calculated.

[0039] 3) Calculate the coordinates of the intersection point (x, y) using the slope and intercept parameters of the lines before and after the intersection. JD ,y JD The formulas for curve deflection angle α are as follows:

[0040]

[0041]

[0042] In the formula, k1 and k3 are the slopes of the front and rear clamping lines, respectively; k2 and k4 are the intercepts of the front and rear clamping lines, respectively.

[0043] 4) Based on the results of the rough segmentation, and using the circular curve distance equation, the orthogonal least squares method is used to fit the curve to obtain the coordinates of the circle center (x). c ,y c ) and the radius R of the circular curve c .

[0044] 5) Calculate the coordinates of the straight-to-curve point (X) using the intersection coordinates and the curve deflection angle. ZH ,Y ZH ):

[0045]

[0046] In the formula, It is the coordinate azimuth angle from the intersection point to the straight-curve point, which can be calculated from the slope of the straight lines before and after; T is the tangent length of the circular curve.

[0047] Similarly, the coordinates of the transition point (X) can be calculated. HZ ,Y HZ ).

[0048] 6) The coordinates of the transition point (X) can be calculated using the coordinates of the center of the circle and the radius of the circular curve. HY ,Y HY ):

[0049]

[0050] In the formula, (x c ,y c ) represents the coordinates of the center of the circle; φ represents the azimuth angle from the center of the circle to the transition point.

[0051] Similarly, the coordinates of the curve point (X) can be calculated. YH ,Y YH ).

[0052] 7) Based on the calculated coordinates of the feature points, re-segment the line containing the measuring points.

[0053] 8) Repeat steps 2) to 7) until the coordinate difference of the same feature point calculated in two steps is less than a certain threshold (the threshold can be 0.1m). The iteration ends at this point, and the position of the feature point is stable.

[0054] 9) Based on the positions of the four characteristic points after stabilization, and the known starting mileage of the line, the mileages of the straight-to-gradient point, the gradual-to-round point, the round-to-gradient point, and the gradual-to-straight point can be calculated. The calculation formula is as follows:

[0055]

[0056] In the formula, L QD d1 is the starting mileage of the line; d1 is the mileage from the straight-to-gradient point to the starting point; l1 is the length of the first transition curve; L0 is the length of the circular curve; l2 is the length of the second transition curve.

[0057] S2: The measured coordinates of straight line segments in the measurement coordinate system are expressed by a linear function, while the measured coordinates of transition curve / circular curve segments in the measurement coordinate system are expressed as functions of independent coordinates in the tangent coordinate system. The linear function includes the measured coordinates, slope, and intercept. The tangent coordinate system is a rectangular coordinate system with the point where the railway line transitions from a straight line to a transition point / from a transition point to a straight line as the origin, the tangent pointing towards the corresponding intersection point as the x-axis, and the direction perpendicular to the tangent and pointing towards the center of the circle as the y-axis. Independent coordinates in the tangent coordinate system are expressed by the equations of the transition curve / circular curve.

[0058] In a specific embodiment, the transition curve equation / circular curve equation is the transition curve / circular curve equation of the curve surveyed using the tangent offset method. The transition curve equation includes the transition curve length, the circular curve radius, and the curve length from the measuring point on the transition curve to the straight-to-transition point / transition-to-straight point. The circular curve equation includes the transition curve length, the circular curve radius, the curve length from the measuring point on the circular curve to the straight-to-transition point / transition-to-straight point, the tangent angle of the transition curve, the perpendicular distance, and the inward displacement of the circular curve.

[0059] In a specific embodiment, the equations of the measuring coordinates of the measuring points within the segmented intervals, specifically the front and rear clamping lines, can be expressed using either the east coordinate function of the measuring points' measuring coordinates to represent the north coordinates, or vice versa. The parameters to be estimated in the former case are the slope, intercept, and east coordinate, while those in the latter case are the slope, intercept, and north coordinate.

[0060] In a specific embodiment, the measured coordinates of the transition curve segment / circular curve segment in the measurement coordinate system are expressed as a function of independent coordinates in the tangent coordinate system. This function is a coordinate transformation model between the measured coordinates of the first transition curve segment / second transition curve segment / circular curve segment in the measurement coordinate system and the independent coordinates in the tangent coordinate system. Substituting the expressions for the independent coordinates of the tangent coordinate system of the measured points of the first transition curve segment and circular curve segment in the tangent coordinate system (with the straight-to-turn point as the origin) into the coordinate transformation model and eliminating the independent coordinates in the tangent coordinate system, a system of equations is obtained that includes the radius of the circular curve, the length of the transition curve, the tangent azimuth of the straight-to-turn point, the measured coordinates of the straight-to-turn point, and the curve length from the measured point to the straight-to-turn point, collectively expressing the measured coordinates of each measured point. Substituting the expression for the independent coordinates of the tangent coordinate system of the measuring points on the second transition curve segment with the transition point as the origin into the coordinate transformation model, and eliminating the independent coordinates of the tangent coordinate system, we can obtain a set of equations that together express the measured coordinates of each measuring point, including the radius of the circular curve, the length of the transition curve, the azimuth of the tangent at the transition point, the measured coordinates of the transition point, and the curve length from the measuring point to the transition point.

[0061] The measured coordinates are the true values, while the actual measured coordinates are values ​​with errors.

[0062] In one specific embodiment, the coordinate transformation model can be a planar four-parameter transformation model.

[0063] In a specific embodiment, the equation of the circular curve segment can be selected from one of the following: the circular curve distance equation, the circular curve parameter equation, and the circular curve tangent coordinate system equation.

[0064] The equation for the distance of a circular curve is an equation that expresses the radius of the circular curve as the distance from the measuring point to the center of the circle. The formula for the distance of a circular curve is:

[0065] (x i -x c ) 2 +(y i -y c ) 2 =R c 2 (6)

[0066] In the formula, (x i ,y i (x) represents the coordinates of the measuring points on the circular curve segment; c ,y c ) represents the coordinates of the center of the circle; R c Let be the radius of the circular curve.

[0067] The parametric equation of a circular curve is an equation that expresses the coordinates of the measuring point using the measured coordinates of the center, the radius of the circular curve, and the central angle from the measuring point to the center. The parametric equation of the circular curve is:

[0068]

[0069] In the formula, It is the azimuth angle from the center of the circle to the measuring point.

[0070] The equation of the circular curve tangent coordinate system is an equation that uses the curve length from the measuring point to the straight-out point to express the tangent coordinates of the measuring point in the tangent coordinate system of the line. The equation of the independent tangent coordinate system of the circular curve is:

[0071]

[0072] In the formula, l i is the curve length from the measuring point to the transition point; l0 is the length of the transition curve; m is the tangent-perpendicular distance; p is the inward displacement of the circular curve; β0 is the tangent angle of the transition curve.

[0073] S3: Linearize the measured coordinate function and list the error equations for the measured coordinates of the corresponding line segments.

[0074] In a specific embodiment, if the corresponding line segment includes a preceding straight line segment, then the error equation for the measured coordinates of the preceding straight line segment is listed; if it includes a following straight line segment, then the error equation for the measured coordinates of the following straight line segment is listed; if it includes a first transition curve segment, then the error equation for the measured coordinates of the first transition curve segment is listed; if it includes a circular curve segment, then the error equation for the measured coordinates of the circular curve segment is listed; if it includes a second transition curve segment, then the error equation for the measured coordinates of the second transition curve segment is listed. The parameters to be estimated in the error equation for the measured coordinates of the straight line segment include one or more of the following: slope, intercept, and coordinates. Depending on whether the straight line segment is preceded or followed by a straight line segment, the slope and intercept can be categorized as the slope of the preceding straight line segment and the intercept of the preceding straight line segment, or the slope of the following straight line segment and the intercept of the following straight line segment. The coordinates are one or more of the north coordinates and east coordinates of the measuring point; the parameters to be estimated in the error equation of the measured coordinates of the transition curve segment include one or more of the following: azimuth of the tangent at the straight-to-transition point / azimuth of the tangent at the transition-to-straight point, radius of the circular curve, length of the first / second transition curve, measured coordinates of the straight-to-transition point / measured coordinates of the transition-to-straight point, and curve length from the measuring point on the first transition curve to the straight-to-transition point / from the measuring point on the second transition curve to the transition-to-straight point.

[0075] In one specific embodiment, the parameters to be estimated in the error equation of the measured coordinates of the first transition curve segment include the azimuth angle of the tangent at the straight-to-transition point, the radius of the circular curve, the length of the first transition curve, the measured coordinates of the straight-to-transition point, and the curve length from the measured point on the first transition curve segment to the straight-to-transition point. The parameters to be estimated in the error equation of the second transition curve segment include the azimuth angle of the tangent at the transition-to-straight point, the radius of the circular curve, the length of the second transition curve, the measured coordinates of the transition-to-straight point, and the curve length from the measured point on the second transition curve segment to the transition-to-straight point.

[0076] In a specific embodiment, the error equation for the measured coordinates of the circular curve segment is one of the following: the circular curve distance error equation, the circular curve parameter error equation, or the circular curve tangent coordinate system error equation. Specifically, if the circular curve distance error equation is used, the parameters to be estimated in the circular curve segment error equation include the measured coordinates of the center and the radius of the circular curve; if the circular curve parameter error equation is used, the parameters to be estimated in the circular curve segment error equation include the measured coordinates of the center, the radius of the circular curve, and the central angle from each point on the circular curve segment to the center; if the circular curve tangent coordinate system error equation is used, the corresponding parameters to be estimated in the circular curve segment error equation include one or more of the following: the azimuth angle of the tangent at the straight-to-curve point / the azimuth angle of the tangent at the transition point, the radius of the circular curve, the length of the transition curve, the measured coordinates of the straight-to-curve point / the measured coordinates of the transition point, and the curve length from the measured point on the circular curve segment to the straight-to-curve point / the transition point.

[0077] S4: Establish length constraints and / or slope and azimuth constraints for the relationship between adjacent line elements in the railway horizontal alignment. The length constraint is an equivalent constraint relationship that converts the theoretical value of the measured coordinate difference between the starting straight-to-curve point and the ending round-to-round point / starting straight-to-curve point and the ending round-to-curve point of a transition curve segment into the tangent coordinates of the round-to-round point / round-to-curve point. The slope and azimuth constraints are equivalent constraint relationships that convert the slope of a straight line segment into the azimuth angle of the horizontal axis of the tangent coordinate system of adjacent transition curve segments.

[0078] Length constraints include one or more of the length constraints of the first transition curve length and the second transition curve length. Tangent coordinates are independent coordinates in the tangent coordinate system.

[0079] The length constraint of the first transition curve is to convert the measured coordinate difference between the starting point of the first transition curve segment (straight-to-gradient) and the ending point of the transition curve (round-to-round) into the tangent coordinate relationship of the transition curve point. The length constraint of the second transition curve is to convert the measured coordinate difference between the starting point of the second transition curve segment (straight-to-gradient) and the ending point of the second transition curve segment (round-to-gradient) into the tangent coordinate relationship of the round-to-gradient point.

[0080] In one specific embodiment, the length constraint is expressed as follows.

[0081] The first transition curve length constraint (taking the curve right skew as an example) is:

[0082]

[0083] In the formula, (X HY ,Y HY ) are the measured coordinates of the transition point.

[0084] Similarly, the second transition curve has a length constraint:

[0085]

[0086] In the formula, (X YH ,Y YH ) are the measured coordinates of the curve point.

[0087] The slope and azimuth constraints include one or more of the following: the relationship between the slope of the first clamping line and the azimuth of the tangent at the point where the first transition curve segment is straight and the relationship between the slope of the second clamping line and the azimuth of the tangent at the point where the second ... third transition curve segment.

[0088] In a specific embodiment, the slope and azimuth constraints are described as follows.

[0089] The relationship between the slope of the first straight line and the azimuth angle of the tangent at the point of transition of the first transition curve segment is as follows:

[0090]

[0091] In the formula, k1 is the slope of the front clamping line; α ZH The azimuth angle of the tangent at the straight-ramp point.

[0092] Similarly, the relationship between the slope of the straight line and the azimuth angle of the tangent at the transition point of the second transition curve segment is as follows:

[0093]

[0094] In the formula, k3 is the slope of the back clamp line; α HZ The azimuth angle of the tangent at the point of gradual straightening.

[0095] S5: Calculate the total differential of the parameters to be estimated in the length constraint and / or slope and azimuth constraint to obtain the error equation. The parameters to be estimated in the length constraint include one or more of the parameters to be estimated in the length constraint of the first transition curve segment and the length constraint of the second transition curve segment. The parameters to be estimated in the slope and azimuth constraint include one or more of the parameters to be estimated in the relationship between the slope of the preceding straight line and the azimuth of the tangent at the transition point of the first transition curve segment, and the relationship between the slope of the following straight line and the azimuth of the tangent at the transition point of the second transition curve segment.

[0096] The parameters to be estimated for the length constraint of the first transition curve segment include one or more of the following: the measured coordinates of the straight-to-transition point, the measured coordinates of the transition-to-circle point, the azimuth angle of the tangent at the straight-to-transition point, the length of the first transition curve, and the length of the circular curve. The parameters to be estimated for the length constraint of the second transition curve segment include one or more of the following: the measured coordinates of the transition-to-straight point, the measured coordinates of the circle-to-transition point, the azimuth angle of the tangent at the transition-to-straight point, the length of the second transition curve, and the length of the circular curve.

[0097] In one specific embodiment, the length constraint error equation is expressed as follows.

[0098] The first transition curve length constraint error equation (taking right skew as an example) is:

[0099]

[0100] In the formula,

[0101]

[0102]

[0103]

[0104]

[0105]

[0106] The superscript 0 indicates an approximate value.

[0107] The error equation for the length constraint of the second transition curve is:

[0108]

[0109] In the formula,

[0110]

[0111]

[0112]

[0113]

[0114]

[0115] The superscript 0 indicates an approximate value.

[0116] The parameters to be estimated for the relationship between the slope of the first clamping line and the azimuth angle of the tangent at the straight-to-straight point of the first transition curve segment include one or more of the slope of the first clamping line and the azimuth angle of the tangent at the straight-to-straight point. The parameters to be estimated for the relationship between the slope of the second clamping line and the azimuth angle of the tangent at the transition-to-straight point of the second transition curve segment include one or more of the slope of the second clamping line and the azimuth angle of the tangent at the transition-to-straight point.

[0117] In a specific embodiment, the slope and azimuth constraint error equations are expressed as follows.

[0118] The constraint error equations for the slope of the first straight line and the azimuth angle of the tangent at the transition point of the first transition curve segment are as follows:

[0119]

[0120] In the formula,

[0121] The constraint error equations for the slope of the rear straight line and the azimuth angle of the tangent at the transition point of the second transition curve segment are as follows:

[0122]

[0123] In the formula,

[0124] S6: Simultaneously solve the error equations for the measured coordinates, length constraint error equations, and / or slope and azimuth constraint error equations on the line segment to be adjusted, and obtain the parameters to be estimated to obtain the optimized railway line. The solution method includes one of the following: conventional least squares method, orthogonal least squares method, overall / total least squares method, weighted overall / total least squares method, and constrained overall / total least squares method.

[0125] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A holistic optimization method considering the relationship between adjacent elements of a railway horizontal alignment, characterized in that, Includes the following steps: S1: Divide the railway line to be adjusted into sections; S2: The measured coordinates of a straight line segment in the measurement coordinate system are expressed by a straight line function, and the measured coordinates of a transition curve segment / circular curve segment in the measurement coordinate system are expressed as a function of independent coordinates in the tangent coordinate system; S3: Linearize the measured coordinate function and list the error equations for the measured coordinates of the corresponding line segments; S4: Establish length constraints and / or slope and azimuth constraints for the relationship between adjacent line elements of the railway horizontal alignment; the length constraints include length constraints for the length of the first transition curve and / or length constraints for the length of the second transition curve, wherein the length constraint for the length of the first transition curve is: the coordinate difference obtained by subtracting the coordinates of the straight transition point from the measured coordinates of the transition circle point, and the coordinates obtained after coordinate transformation are equal to the coordinates of the tangent of the transition circle point; the length constraint for the length of the second transition curve is: the coordinate difference obtained by subtracting the measured coordinates of the transition straight point from the measured coordinates of the circle transition point, and the coordinates obtained after coordinate transformation are equal to the coordinates of the tangent of the circle transition point; the slope and azimuth constraints are conversion constraint relationships between the slope of the straight line segment and the tangent azimuth of the adjacent transition curve segment, including one or more of the conversion constraint relationships between the slope of the preceding straight line and the tangent azimuth of the straight transition point of the first transition curve segment, and the conversion constraint relationships between the slope of the following straight line and the tangent azimuth of the transition straight point of the second transition curve segment; S5: Take the total differential of the parameters to be estimated in the length constraint and / or slope and azimuth constraint to obtain the error equation; S6: Solve the error equations of the measured coordinates, length constraint error equations, and / or slope and azimuth constraint error equations on the line segment to be adjusted, and obtain the optimized railway line.

2. The overall optimization method for considering the relationship between adjacent elements of railway horizontal alignment according to claim 1, characterized in that, In step S1, the railway line includes two or more of the following adjacent segments: the straight section before the railway line, the first transition curve section, the circular curve section, the second transition curve section, and the straight section after the railway line.

3. The overall optimization method for considering the relationship between adjacent elements of railway horizontal alignment according to claim 1, characterized in that, In step S2, the linear function includes measured coordinates, slope, and intercept. The tangent coordinate system is a rectangular coordinate system with the straight-to-gradient point / gradual-to-straight point of the railway line as the origin, the tangent pointing in the direction of the corresponding intersection point as the x-axis, and the direction perpendicular to the tangent and pointing in the direction of the circle as the y-axis. The independent coordinates in the tangent coordinate system are expressed by the transition curve equation / circular curve equation.

4. The overall optimization method for considering the relationship between adjacent line elements in railway horizontal alignment according to claim 3, characterized in that, The transition curve equation / circular curve equation is the transition curve / circular curve equation of the curve surveyed by the tangent offset method.

5. The overall optimization method for considering the relationship between adjacent elements of railway horizontal alignment according to claim 4, characterized in that, The equation of the transition curve includes the length of the transition curve, the radius of the circular curve, and the curve length from the measuring point on the transition curve to the straight-to-transition point / transition-to-straight point. The equation of the circular curve includes the length of the transition curve, the radius of the circular curve, the curve length from the measuring point on the circular curve to the straight-to-transition point / transition-to-straight point, the tangent angle of the transition curve, the perpendicular distance, and the inward displacement of the circular curve.

6. The overall optimization method for considering the relationship between adjacent elements of railway horizontal alignment according to claim 1, characterized in that, In step S3, if the corresponding line segment includes a front clamping straight line segment, then the error equation for the measured coordinates of the front clamping straight line segment is listed; if it includes a rear clamping straight line segment, then the error equation for the measured coordinates of the rear clamping straight line segment is listed; if it includes a first transition curve segment, then the error equation for the measured coordinates of the first transition curve segment is listed; if it includes a circular curve segment, then the error equation for the measured coordinates of the circular curve segment is listed; if it includes a second transition curve segment, then the error equation for the measured coordinates of the second transition curve segment is listed.

7. The overall optimization method for considering the relationship between adjacent elements of railway horizontal alignment according to claim 6, characterized in that, The parameters to be estimated in the error equation of the measured coordinates of the first clamping straight line segment include one or more of the following: the slope of the first clamping straight line, the intercept of the first clamping straight line, and coordinates. The parameters to be estimated in the error equation of the measured coordinates of the second clamping straight line segment include one or more of the following: the slope of the second clamping straight line, the intercept of the second clamping straight line, and coordinates. The coordinates are one or more of the north coordinates and east coordinates of the measuring point. The parameters to be estimated in the error equation of the measured coordinates of the first transition curve segment include the azimuth of the tangent at the straight-to-transition point, the radius of the circular curve, the length of the first transition curve, the measured coordinates of the straight-to-transition point, and the distance from the measuring point on the first transition curve to the straight line. The parameters to be estimated in the error equation of the second transition curve segment include one or more of the following: the azimuth of the tangent at the transition point, the radius of the circular curve, the length of the second transition curve, the measured coordinates of the transition point, and the length of the curve from the measured point on the second transition curve to the transition point. The parameters to be estimated in the error equation of the circular curve segment include one or more of the following: the azimuth of the tangent at the transition point / the azimuth of the tangent at the transition point, the radius of the circular curve, the length of the transition curve, the measured coordinates of the transition point / the measured coordinates of the transition point, and the length of the curve from the measured point on the circular curve to the transition point / the length of the curve from the measured point on the circular curve to the transition point / the length of the curve from the transition point.

8. The overall optimization method for considering the relationship between adjacent elements of railway horizontal alignment according to claim 1, characterized in that, In step S4, the length constraint includes one or more of the length constraints of the first transition curve length and the second transition curve length; the tangent coordinates are coordinates in the tangent coordinate system; and the slope and azimuth constraints include one or more of the relationship between the slope of the preceding straight line and the azimuth of the tangent at the transition point of the first transition curve segment, and the relationship between the slope of the following straight line and the azimuth of the tangent at the transition point of the second transition curve segment; wherein, the relationship between the slope of the preceding straight line and the azimuth of the tangent at the transition point of the first transition curve segment is as follows: k1 is the slope of the preceding straight line, α ZH The azimuth angle of the tangent at the transition point is given; the relationship between the slope of the subsequent straight line and the azimuth angle of the tangent at the transition point of the second transition curve segment is given. k3 is the slope of the back straight line, α HZ The azimuth angle of the tangent at the point of gradual straightening.

9. The overall optimization method for considering the relationship between adjacent line elements in railway horizontal alignment according to claim 1, characterized in that, In step S5, the estimated parameters of the length constraint include one or more of the estimated parameters of the first transition curve segment length constraint and the second transition curve segment length constraint. The estimated parameters of the first transition curve segment length constraint include one or more of the measured coordinates of the straight-to-turn point, the measured coordinates of the transition-to-circle point, the azimuth angle of the tangent at the straight-to-turn point, the length of the first transition curve, and the length of the circular curve. The estimated parameters of the second transition curve segment length constraint include one or more of the measured coordinates of the transition-to-straight point, the measured coordinates of the circle-to-turn point, the azimuth angle of the tangent at the transition-to-straight point, the length of the second transition curve, and the length of the circular curve. The parameters to be estimated for the ratio and azimuth constraint include one or more of the following: the relationship between the slope of the preceding clamping line and the azimuth angle of the tangent at the straight-to-straight point of the first transition curve segment; and the relationship between the slope of the following clamping line and the azimuth angle of the tangent at the straight-to-straight point of the second transition curve segment. The parameters to be estimated for the relationship between the slope of the preceding clamping line and the azimuth angle of the tangent at the straight-to-straight point of the first transition curve segment include one or more of the following: the slope of the preceding clamping line and the azimuth angle of the tangent at the straight-to-straight point. The parameters to be estimated for the relationship between the slope of the following clamping line and the azimuth angle of the tangent at the straight-to-straight point of the second transition curve segment include one or more of the following: the slope of the following clamping line and the azimuth angle of the tangent at the straight-to-straight point.

10. The overall optimization method for considering the relationship between adjacent line elements in railway horizontal alignment according to claim 1, characterized in that, In step S6, the method for solving the parameters to be estimated includes one of the following: conventional least squares method, orthogonal least squares method, global / total least squares method, weighted global / total least squares method, and constrained global / total least squares method.

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