Railway line plane line shape digital construction method

Abstract

The invention relates to the technical field of railway line digitization, in particular to a railway line plane line shape digitization construction method, which comprises the following steps of: dividing a base line into a plurality of straight line elements and two continuous curve line elements connected between two adjacent straight line elements, and calculating the curve length and tangent length of the curve line elements; the calculated curve length and tangent length can be used for calculating the mileage, coordinates and tangent azimuth angle of the main point to obtain the corresponding relation between the coordinates of the main point and the mileage, and then the corresponding relation between other mileages and coordinates of the base line is calculated based on the main point to form the corresponding relation between all the mileages and coordinates of the base line; according to the method, the plane linear digital construction of the base line is completed, a two-line plane digital linear model can be constructed according to the base line, the line design is simpler, and the quality of the railway line design in China is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of railway line digitization, and in particular to a method for digitally constructing the plane alignment of a railway line. Background Art

[0002] A railway is a three-dimensional entity. It is a belt-like structure composed of roadbeds, bridges, tunnels, tracks, stations, and facilities along the route. The term "line" describes the railway's position in three dimensions. For ease of study, it is broken down into line plan design, line longitudinal section design, and line cross-sectional design. These three aspects are interrelated and should be considered separately but also comprehensively.

[0003] The track plan describes the projection of the track centerline onto the geoid. Because the inner rail widens on curves, the track centerline is half a track gauge from the center of the outer rail. A vertical section along the track plan and then unfolding it creates a longitudinal section. This section shows how the track top elevation changes with increasing line length.

[0004] On curves, superelevation is required, with different top-of-rail elevations for the inner and outer rails. If only the outer rail is raised, the longitudinal section uses the top-of-rail elevation of the inner rail. If the outer rail is raised and the inner rail is lowered, the longitudinal section uses the center-of-rail elevation.

[0005] The normal section at any point on the line is the cross section of the railway at that point. Line design is the work of determining the spatial position of the line and the geometric dimensions of each part.

[0006] To achieve intelligent line design, the spatial line position must first be digitized. A linear model is a digital description of the line. This requires conceptual abstraction and generalization of line design objects, creating a set of variables that are simple, unified, and easily implemented during the design process to represent the line. Furthermore, a series of algorithms that provide accurate solutions and are easily programmable must be established to support line design.

[0007] The set of variables describing railway alignment can serve as design variables for intelligent route selection. Only by quickly and accurately calculating the spatial position of the railway using a linear model can we determine and address route selection constraints based on the spatial relationship between the line and the environment, lay out structures such as roadbeds, bridges, and tunnels, calculate project operation and maintenance costs, and conduct environmental and safety assessments.

[0008] Therefore, linear digitization is the basis for railway digitization and intelligence. However, the existing technology does not have relevant methods on how to achieve railway linear digitization, which makes railway line design complicated. Therefore, inventing a railway line linear digitization construction method is of great significance to promoting the digitization and intelligence of railway design, construction, operation and maintenance. Summary of the Invention

[0009] The purpose of the present invention is to solve the problem that the existing railway line plane alignment digitization theory is not systematic, which affects the transformation of railway line design to digitalization and intelligence, and to provide a railway line plane alignment digitization construction method.

[0010] In a first aspect, the present invention provides a method for digitally constructing a railway line plane alignment, comprising the steps of constructing a baseline:

[0011] S1. Divide the baseline into a number of straight line elements and two continuous curve line elements connecting two adjacent straight line elements. The curve line elements include circular curve line elements and transition curve line elements connecting the two ends of the circular curve line element. Each curve line element has a corresponding intersection point.

[0012] S2. Calculate the curve length and tangent length of each curve element based on the coordinates of each intersection point, the radius of the circular curve element, and the length of the transition curve element;

[0013] S3. Calculate the main point mileage based on the baseline's starting mileage K0, the distance D1 between the first intersection point JD1 and the baseline's starting mileage K0, the coordinates of each intersection point, the length of each transition curve element, and the curve length and tangent length of each curve element. The main point mileage includes the straight-to-slow point mileage, the transition curve point mileage, the midpoint mileage, the transition curve point mileage, and the transition straight point mileage. The straight-to-slow point mileage is the mileage of the boundary between a straight line element and a transition curve element in the direction of the route. The transition curve point mileage is the mileage of the starting end of a circular curve element. The midpoint mileage is the mileage of the midpoint of a circular curve element. The transition curve point mileage is the mileage of the end of a circular curve element. The transition straight point mileage is the mileage of the boundary between a transition curve element and a straight line element in the direction of the route.

[0014] S4. Calculate the coordinates and tangent azimuth of the principal point based on the latitude and longitude coordinates of each intersection point, the radius of the curve element, the tangent length, and the azimuth of the front tangent line, and obtain the corresponding relationship between the coordinates of the principal point and the mileage;

[0015] S5. Based on the correspondence between the coordinates of the main point and the mileage, the coordinates of other mileages on the baseline and the corresponding mileages are calculated to form the correspondence between all mileages and coordinates of the baseline. The digital construction of the horizontal alignment of the railway line is completed.

[0016] The present invention provides a method for digitally constructing the plane alignment of a railway line. The method divides a baseline into a plurality of straight line elements and two continuous curved line elements connected between two adjacent straight line elements, and calculates the curve length and tangent length of the curved line elements. The calculated curve length and tangent length can be used to calculate the mileage, coordinates and tangent azimuth of a main point, thereby obtaining a correspondence between the coordinates and mileage of the main point. Then, based on the main point, the correspondence between the mileage and coordinates of other parts of the baseline is calculated, thereby forming a correspondence between all mileages and coordinates of the baseline. The digital construction of the plane alignment of the baseline is completed, and the line design is simplified, thereby improving the quality of railway line design in my country.

[0017] Preferably, in step S2, the steps of calculating the curve length and tangent length of each curve element according to the coordinates of each intersection point, the radius of the circular curve element, and the length of the transition curve element are as follows:

[0018] Calculate the deflection angle α of the curve element of the current curve line element through the coordinates of the current intersection point, the previous intersection point and the next intersection point;

[0019] The transition curve element angle β0 of the curve element is calculated based on the transition curve element length l0 of the current curve element and the radius R of the circular curve element. The calculation formula is:

[0020]

[0021] The tangent-vertical distance m and the inward displacement p of the transition curve element are calculated based on the transition curve element length l0, the circular curve element radius R and the transition curve element rotation angle β0 of the current curve element. The calculation formula is:

[0022]

[0023] The tangent length T of the current curve element is calculated based on the circular curve element radius R, inward displacement p, deflection angle α and tangent-vertical distance m of the current curve element. The calculation formula is:

[0024]

[0025] The curve length L of the current curve element is calculated based on the circular curve element radius R, the deflection angle α and the length l0 of the transition curve element. The calculation formula is:

[0026]

[0027] In the above calculation, since the calculation of the tangent-perpendicular distance m and the inward displacement p of the transition curve line element is more accurate than the existing technology, the calculation results of the tangent length T of the curve line element, the curve length L of the curve line element and the outward vector distance E of the curve line element are more accurate, and the results of the subsequent main point mileage calculation are more accurate, thereby improving the quality of the linear design.

[0028] Preferably, the steps for calculating the main point mileage are as follows:

[0029] According to the starting mileage K0 of the baseline, the distance D1 between the first intersection point JD1 and the starting mileage K0 of the baseline, the tangent length T1 of the curve element corresponding to the first intersection point JD1, and the length l of the curve element 01 and the curve length L1, the plane distance D between the i-th and i-1-th intersection points i The tangent length T of the curve element corresponding to the i-th intersection point i , curve element length l 0i and curve length L i Calculate the mileage of the first straight-line point Slow dot mileage Mileage at the midpoint Round trip mileage Gentle straight mileage and the mileage of the i-th straight slow point Slow dot mileage Mileage at the midpoint Round trip mileage Gentle straight mileage i>1.

[0030] Preferably, the first straight-slow point mileage is calculated based on the starting mileage K0 of the baseline, the distance D1 between the first intersection point JD1 and the starting mileage K0 of the baseline, and the tangent length T1 of the curve element corresponding to the first intersection point JD1. The calculation formula is as follows:

[0031]

[0032] According to the plane distance D between the i-th and i-1-th intersection points i , the tangent length T of the curve element corresponding to the i-1th intersection point i-1 The tangent length T of the curve element corresponding to the i-th intersection point i Calculate the length of the front straight line of the i-th intersection i>1;

[0033] According to the straightening point of the curve element corresponding to the previous intersection point The length of the straight line before the i-th intersection point Calculate the mileage of the i-th straight-slow point

[0034] According to the mileage of the i-th straight slow point and the curve element length l 0i Calculate the mileage of the i-th slow circle point

[0035] According to the mileage of the i-th slow circle point and the curve length l iCalculate the mileage of the i-th curve midpoint as half of

[0036] According to the i-th midpoint Curve length L i and the curve element length l 0i Calculate the mileage of the i-th circle slow point

[0037] According to the straight and slow point mileage of the curve line element corresponding to the current intersection and curve length L i Calculate the mileage of the i-th straightening point

[0038] Among them, the front clip straight line length Mileage of the i-th straight-slow point Slow dot mileage Mileage at the midpoint Round trip mileage Gentle straight mileage The calculation formula is as follows:

[0039]

[0040] Preferably, calculating the coordinates of the principal point and the tangent azimuth includes:

[0041] According to the latitude and longitude coordinates (X i ,Y i ), curve element radius R i , tangent length T i and the front tangent azimuth A i Calculate the mileage of the i-th straight-slow point Mileage of the i-th slow circle point i midpoint mileage Mileage of the i-th circle slow point and the mileage of the i-th straightening point Coordinates and tangent azimuth of

[0042] Mileage of straight and slow points within the i-th intersection coordinate Tangent azimuth The calculation is as follows:

[0043]

[0044] Mileage of straight and slow points within the i-th intersection coordinate Tangent azimuth The calculation is as follows:

[0045]

[0046] Mileage of the slow circle point within the i-th intersection coordinate Tangent azimuth The calculation is as follows:

[0047]

[0048] Where: —The straight-line distance between the circular slow point HY and the straight slow point ZH; —The rectangular coordinate of point HY in the coordinate system with point ZH as the origin; —Tangent azimuth at point HY; —H-Y point coordinates; ±—the curve is - for left deviation and + for right deviation;

[0049] Mileage of the slow circle point within the i-th intersection coordinate Tangent azimuth The calculation is as follows:

[0050]

[0051] Where: —The straight-line distance between the circular slow point YH and the straight-line slow point HZ; —The rectangular coordinate of point YH in the coordinate system with point HZ as the origin; —Tangent azimuth at point YH; —YH point coordinates; ±—If the curve deviates to the left, take -; if it deviates to the right, take +.

[0052] Preferably, the coordinates of other baseline miles and their corresponding miles are calculated based on the correspondence between the coordinates of the principal point and the miles, and the steps are as follows:

[0053] Given any point on the baseline, compare the mileage with the previously calculated main point mileage to determine the line element on which the point is located, and perform calculations based on the line element:

[0054] (1) When the line element where the point is located is on the straight line element: the mileage of any point P on the straight line element is K P , according to the starting point HZ of the straight line i-1 and the corresponding azimuth angle A i Calculate the coordinates of point P. The calculation steps are as follows:

[0055]

[0056] Where: ΔK is the mileage difference between point P and point HZ within the range of the i-1th intersection; X P 、Y P —Latitude and longitude coordinates of point P; —The latitude and longitude coordinates of HZ within the i-1th intersection; Ai —the azimuth between the i-1th and i-th intersection points;

[0057] (2) When the line element of the point is located on the circular curve line element: within the i-th intersection range, any point P on the circular curve line element has a mileage of K P , first calculate the distance from point P to the beginning of the circular curve HY i The arc length ΔK of point P is calculated, and then the chord angle α at point P and the chord length from P to the beginning of the circular curve are calculated. The calculation method is as follows:

[0058]

[0059] Where: —The mileage of the starting point of the circular curve, that is, the mileage of point HY; ΔK—the distance from the calculation point P to the starting point HY of the circular curve i Arc length of a point; R i — radius of the circular curve; α, Φ — chord tangent angle and central angle at point P; —The length of the chord from P to the beginning of the circular curve;

[0060] The latitude and longitude coordinates of the final calculated point (X P ,Y P ) and tangent azimuth angle α P :

[0061]

[0062] Where: —Latitude and longitude coordinates of the starting point of the circular curve; —the tangent azimuth at the beginning of the circular curve; α P - tangent azimuth at any point P on the circular curve; ± - right turn is +, left turn is -;

[0063] (3) When the line element where the point is located is located on the transition curve line element, determine whether the point is located on the front transition curve line element or the back transition curve line element in front of the circular curve line element;

[0064] 1) When point P is on the front transition curve element, the calculation method is as follows:

[0065]

[0066] Where: - The latitude and longitude coordinates of the ZH point of the front transition curve element; L P - Calculation points P to ZH i The length of the point; x P ,y P —The coordinates of point P in the rectangular coordinate system of the transition curve element; α P - tangent azimuth at any point P on the front transition curve element; -ZH i The tangent azimuth at the point; ±—the curve deviates to the left and takes -, and right takes +;

[0067] 2) When point P is on the post-transition curve, the calculation method is as follows:

[0068]

[0069] Where: - Latitude and longitude coordinates of the HZ point of the post-transition curve element; L P - Calculation point P to HZ i The length of the point; x P ,y P —The coordinates of point P in the rectangular coordinate system of the transition curve element: α P - tangent azimuth at any point P on the post-transition curve; -HZ i The tangent azimuth at the point; ±—+ for left deviation of the curve, - for right deviation.

[0070] Preferably, in step S5, after forming the correspondence between all the mileages and coordinates of the baseline, the second line construction step is also included:

[0071] With reference to the baseline, the parallel or winding relationship of the second line relative to the baseline is given. Through the line section reference relationship matrix and the intersection reference relationship matrix, the mileage and coordinate relationship of the second line are calculated, and the digital construction of the railway line plane alignment is completed.

[0072] Preferably, in the construction of the second line, the reference relationship between the intersection of the second line and the intersection of the baseline is divided into two categories: parallel and detour. The intersection types of the parallel line include: parallel and parallel intersection, parallel and non-parallel intersection, S-bend intersection before and S-bend intersection; the detour intersection types include: detour starting intersection, detour middle intersection, detour ending intersection, and single detour intersection.

[0073] All types of intersection data can be represented by the following unified six-dimensional vector:

[0074] JD'=[TJD',RJD',U,V,T',l'0] T ; (2-20)

[0075] Among them, U and V corresponding to various intersection points are shown in Table 1:

[0076]

[0077] By combining all the intersection column vectors in the order of increasing mileage, we can obtain the reference relationship matrix of the intersection points of the entire second-line route as follows:

[0078]

[0079] The parallel and bypass reference relationship of the second-line reference baseline can be expressed by the following segment reference relationship vector r:

[0080] r=[T',K S ,K E ,JD S ,JD E ] T ; (2-22)

[0081] Where T' is the section reference relationship type, including parallel and detour, K S , K E JD is the starting and ending mileage of the section. S , JD E Number the starting and ending intersection points of the section;

[0082] The entire second line is connected by staggered parallel and detour sections, and all local reference relationship vectors r1, r2, ..., r m After sorting by mileage and then combining, a matrix M reflecting the reference relationship of the route can be formed. R ';

[0083]

[0084] Combined with M R ' and M RJD 'A reference linear model can be established to calculate the geometric parameters and mileage of the second-line line.

[0085] In a second aspect, the present invention provides a system for digitally constructing the plane alignment of a railway line, comprising at least one processor and a memory communicatively connected to the at least one processor; the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute the method for digitally constructing the plane alignment of a railway line.

[0086] In a third aspect, the present invention provides a computer-readable medium having stored thereon instructions executable by a processor, wherein when the instructions are executed by the processor, the processor executes the method for digitally constructing the plane alignment of a railway line.

[0087] Compared with the prior art, the present invention has the following beneficial effects:

[0088] 1. The present invention provides a method for digitally constructing the plane alignment of a railway line. The method divides a baseline into a number of straight line elements and two continuous curved line elements connecting two adjacent straight line elements, and calculates the curve length and tangent length of the curved line elements. The calculated curve length and tangent length are then used to calculate the mileage, coordinates, and tangent azimuth of the main point, thereby obtaining the correspondence between the coordinates and mileage of the main point. The correspondence between the mileage and coordinates of other parts of the baseline is then calculated based on the main point, forming a correspondence between all mileage and coordinates of the baseline. This completes the digital construction of the plane alignment of the baseline, simplifies line design, and improves the quality of railway line design in my country.

[0089] 2. The present invention provides a railway line plane alignment digital construction system, which can execute instructions of the railway line plane alignment digital construction method through a processor.

[0090] 3. The present invention provides a computer-readable medium storing instructions for a method for digitally constructing the plane alignment of a railway line that can be executed by a processor. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] Figure 1 This is a schematic diagram of the railway plane line;

[0092] Figure 2 Calculate the schematic diagram for the curve element;

[0093] Figure 3 Schematic diagram for calculating the main point mileage of the intermediate intersection;

[0094] Figure 4 This is the schematic diagram for calculating the main point mileage of the first intersection;

[0095] Figure 5 It is a schematic diagram of the properties of the transition curve;

[0096] Figure 6 This is a schematic diagram of HY point coordinate calculation;

[0097] Figure 7 This is a schematic diagram of railway line mileage;

[0098] Figure 8 Schematic diagram for line selection;

[0099] Figure 9 Schematic diagram for calculating the geodetic coordinates of point P;

[0100] Figure 10 Schematic diagram of the coordinates and azimuth of point P;

[0101] Figure 11 Parallel intersection diagram Figure 1 ;

[0102] Figure 12 Parallel intersection diagram Figure 2 ;

[0103] Figure 13 Schematic diagram of the intersection point before and after the S-bend;

[0104] Figure 14 Schematic diagram of the starting intersection, middle intersection and ending intersection of the detour section;

[0105] Figure 15 This is a schematic diagram of a single detour intersection;

[0106] Figure 16 Determine the schematic diagram for the starting point of the detour section;

[0107] Figure 17 This is a schematic diagram of bypassing the broken chain;

[0108] Figure 18 Schematic diagram of mileage coordinate conversion. DETAILED DESCRIPTION

[0109] The present invention will be further described in detail below with reference to specific embodiments. However, this should not be construed as limiting the scope of the present invention to the following embodiments, as all technologies implemented based on the present invention fall within the scope of the present invention.

[0110] Unless otherwise specified, in the description of the specific embodiments of the present invention, the terms indicating the orientation or positional relationship, such as "upper", "lower", "left", "right", "center", "inside", and "outside", are based on the expressions of the orientation or positional relationship shown in the accompanying drawings, or are the orientation or positional relationship in which the invented product / device / apparatus is placed when it is conventionally used. These terms of orientation or positional relationship are merely for the purpose of facilitating the description of the scheme of the present invention or simplifying the description of the specific embodiments to facilitate the rapid understanding of the scheme by technicians, and do not indicate or imply that a specific device / component / element must have a specific orientation, or be constructed and operated in a specific positional relationship, and therefore should not be understood as limiting the present invention.

[0111] In addition, if the terms "horizontal", "vertical", "overhanging", "parallel" and the like appear, it does not mean that the corresponding devices / components / elements are required to be absolutely horizontal or vertical or overhanging or parallel, but may be slightly tilted or have deviations. For example, "horizontal" only means that its direction is more horizontal than "vertical", and does not mean that the structure must be completely horizontal, but may be slightly tilted. Alternatively, it can be simply understood that the corresponding devices / components / elements are set in directions such as "horizontal", "vertical", "overhanging", and "parallel", and can have an error / deviation of ±10% relative to the corresponding direction setting, more preferably an error / deviation within ±8%, more preferably an error / deviation within ±6%, more preferably an error / deviation within ±5%, and more preferably an error / deviation within ±4%. As long as the corresponding device / component / element is within the error / deviation range, it can still achieve its role in the solution of the present invention.

[0112] In addition, the expressions “first”, “second”, “third”, etc. in the terms are merely used to distinguish the description of the same or similar components, and should not be understood as emphasizing or implying the relative importance of specific components.

[0113] In addition, in the description of the embodiments of the present invention, "several," "plurality," and "a number" represent at least two. It can also be any number such as two, three, four, five, six, seven, eight, nine, or even more than nine.

[0114] Furthermore, in the description of the technical solution of the present invention, unless otherwise expressly specified, defined, or limited, the terms "disposed," "installed," "connected," "connected," "provided with," "laid," and "arranged" should be understood broadly. For example, they may refer to fixed connections, detachable connections, or integral connections. They may be welded, riveted, bolted, threaded, or other commonly used connection methods in the art. Such connections may be mechanical, electrical, or communicative; they may be direct, indirect via an intermediate medium, or internally connected between two components.

[0115] Example 1

[0116] A method for digitally constructing the horizontal alignment of a railway line includes the steps of constructing a baseline. In double-track railway design, a design line with mileage running from the starting point to the end point is used. Its geometric shape and mileage are completely independent of other lines. In double-track railway designs in my country, this is generally the left line. In single-track railways, there is only one baseline. The steps for constructing a baseline are as follows:

[0117] S1. Divide the baseline into several straight line elements and curve line elements connecting two adjacent straight line elements. The curve line elements include circular curve line elements and transition curve line elements connecting the two ends of the circular curve line elements. Each curve line element corresponds to an intersection point. Figure 1 As shown, JD i and JD i+1 The intersection of the two curve elements is the virtual intersection between the tangent of the front transition curve element and the tangent of the back transition curve element. In this embodiment, JD represents the intersection of the baselines. i Indicates the first i An intersection.

[0118] S2. Calculate the curve length and tangent length of each curve element based on the coordinates of each intersection point, the radius of the circular curve element, and the length of the transition curve element, such as Figure 2 As shown in the figure, the curve elements that need to be calculated include the deflection angle α, tangent length T, curve length L and external sagittal distance E. When designing, it is assumed that the starting point, midpoint and intersection point, as well as the curve element length l0 and the circular curve element radius R are set. The calculation steps are as follows:

[0119] The deflection angle α of the curve element of the current curve line element is calculated through the coordinates of the current intersection point, the previous intersection point and the next intersection point; the intersection coordinates are obtained: after the line is designed (that is, after the starting point, end point and intersection point are determined), they are obtained through surveying and design.

[0120] The transition curve element angle β0 of the curve element is calculated based on the transition curve element length l0 of the current curve element and the radius R of the circular curve element. The calculation formula is:

[0121]

[0122] The tangent-vertical distance m and the inward displacement p of the transition curve element are calculated based on the transition curve element length l0, the circular curve element radius R and the transition curve element rotation angle β0 of the current curve element. The calculation formula is:

[0123]

[0124] The tangent length T of the current curve element is calculated based on the circular curve element radius R, inward displacement p, deflection angle α and tangent-vertical distance m of the current curve element. The calculation formula is:

[0125]

[0126] The curve length L of the current curve element is calculated based on the circular curve element radius R, the deflection angle α and the length l0 of the transition curve element. The calculation formula is:

[0127]

[0128] The external vector distance E of the current curve element is calculated based on the circular curve element radius R, the inward displacement p and the deflection angle α of the current curve element. The calculation formula is:

[0129]

[0130] In the above calculation, since the calculation of the tangent-perpendicular distance m and the inward displacement p of the transition curve line element is more accurate than the existing technology, the calculation results of the tangent length T of the curve line element, the curve length L of the curve line element and the outward vector distance E of the curve line element are more accurate, and the results of the subsequent main point mileage calculation are more accurate, thereby improving the quality of the linear design.

[0131] S3. Calculate the main point mileage based on the baseline's starting mileage K0, the distance D1 between the first intersection point JD1 and the baseline's starting mileage K0, the coordinates of each intersection point, the length of each transition curve element, and the curve length and tangent length of each curve element. The main point mileage includes the straight-to-slow point mileage, the transition curve point mileage, the midpoint mileage, the transition curve point mileage, and the transition straight point mileage. The straight-to-slow point mileage is the mileage of the boundary between a straight line element and a transition curve element in the direction of the route. The transition curve point mileage is the mileage of the starting end of a circular curve element. The midpoint mileage is the mileage of the midpoint of a circular curve element. The transition curve point mileage is the mileage of the end of a circular curve element. The transition straight point mileage is the mileage of the boundary between a transition curve element and a straight line element in the direction of the route.

[0132] Correspondingly, such as Figure 3 As shown, the principal points of the curve element include:

[0133] ZH—straight-to-transition point, the dividing point where the line enters the transition curve from a straight line in the forward direction;

[0134] HY—Transition curve point, the dividing point from transition curve to circular curve according to the line forward direction;

[0135] QZ—midpoint of the curve, that is, the midpoint of the circular curve;

[0136] YH—Circular transition point, the dividing point from the circular curve to the transition curve according to the direction of the line;

[0137] HZ—Transition curve point, the dividing point where the line goes from a transition curve to a straight line.

[0138] The steps to calculate the main point mileage are as follows:

[0139] According to the starting mileage K0 of the baseline, the distance D1 between the first intersection JD1 and the starting mileage K0 of the baseline, the tangent length T1 of the curve element corresponding to the first intersection JD1, and the length l of the transition curve element corresponding to the first intersection JD1 01 , the curve length L1 of the curve element corresponding to the first intersection point JD1, the plane distance D between the i-th and i-1-th intersection points i , the tangent length T of the curve element corresponding to the i-th intersection point i , the length of the transition curve element corresponding to the i-th intersection point is l 0i The curve length L of the curve element corresponding to the i-th intersection pointi Calculate the mileage of the first straight-line point First slow-down point mileage First midpoint mileage First round stop mileage First straight point mileage Mileage of the i-th straight-slow point Mileage of the i-th slow circle point Mileage of the i-th midpoint Mileage of the i-th circle slow point Gentle straight mileage i>1 and is a positive integer.

[0140] Specifically, such as Figure 4 As shown, the mileage of the first straight-slow point is calculated based on the starting mileage K0 of the baseline, the distance D1 between the first intersection point JD1 and the starting mileage K0 of the baseline, and the tangent length T1 of the curve element corresponding to the first intersection point JD1. The calculation formula is as follows:

[0141]

[0142] Where: K0—starting mileage of the baseline.

[0143] According to the plane distance D between the i-th and i-1-th intersection points i , the tangent length T of the curve element corresponding to the i-1th intersection point i-1 The tangent length T of the curve element corresponding to the i-th intersection point i Calculate the length of the front straight line of the i-th intersection i>1;

[0144] According to the straightening point of the curve element corresponding to the previous intersection point The length of the straight line before the i-th intersection point Calculate the mileage of the i-th straight-slow point

[0145] According to the mileage of the i-th straight slow point and the curve element length l 0i Calculate the mileage of the i-th slow circle point

[0146] According to the mileage of the i-th slow circle point and curve length L i Calculate the mileage of the i-th curve midpoint as half of

[0147] According to the i-th midpoint Curve length L i and the curve element length l 0i Calculate the mileage of the i-th circle slow point

[0148] According to the straight and slow point mileage of the curve line element corresponding to the current intersection and curve length L i Calculate the mileage of the i-th straightening point

[0149] Among them, the front clip straight line length Mileage of the i-th straight-slow point Slow dot mileage Mileage at the midpoint Round trip mileage Gentle straight mileage The calculation formula is as follows:

[0150]

[0151] Where: D i —the plane distance between the i-th and i-1-th intersection points, where i>1 and is a positive integer; L Zi —The length of the straight line in front of the i-th intersection; T i-1 —The tangent length of the curve element corresponding to the i-1th intersection point, that is, the tangent length of the curve element corresponding to the previous intersection point of the current intersection point in the direction of decreasing baseline mileage; T i —The tangent length of the curve element corresponding to the i-th intersection point, that is, the tangent length of the curve element corresponding to the current intersection point, where i represents the current one and i-1 represents the previous one.

[0152] In the above calculation method, except for the first straight slow point mileage Except for the one that needs to be calculated using formula (1-7), the mileage of other main points can be calculated using formula (1-8).

[0153] S4. Calculate the coordinates and tangent azimuth of the principal point based on the latitude and longitude coordinates of each intersection point, the radius of the curve element, the tangent length, and the azimuth of the front tangent line, and obtain the corresponding relationship between the coordinates of the principal point and the mileage;

[0154] Calculating the coordinates of the principal point and the tangent azimuth includes:

[0155] According to the latitude and longitude coordinates (X i ,Y i ), radius of circular curve element R i , tangent length T i and the front tangent azimuth A i (The azimuth between the i-1th and i-th intersections is calculated based on the longitude and latitude coordinates of the adjacent intersections before and after) Calculate the mileage of the i-th straight-slow point Mileage of the i-th slow circle point i midpoint mileage Mileage of the i-th circle slow point and the mileage of the i-th straightening point Coordinates and tangent azimuth of

[0156] Mileage of straight and slow points within the i-th intersection coordinate Tangent azimuth The calculation is as follows:

[0157]

[0158] Mileage of straight and slow points within the i-th intersection coordinate Tangent azimuth The calculation is as follows:

[0159]

[0160] Since the transition curve generally used in railways is a radial spiral (i.e., a cubic parabola), its basic characteristic is that the product of the curvature radius ρ of any point on the transition curve and the arc length l from the point to the starting point of the transition curve is a constant, that is, ρ·l=A 2 , where A is called the clothoid parameter, τ is the angle between the tangent line at this point and the tangent line at point ZH, and is given by Figure 5 The differential parametric equation of the transition curve is:

[0161] dl=ρ·dτ; (1-11)

[0162] dx=dl·cosτ; (1-12)

[0163] dy=dl·sinτ; (1-13)

[0164] After proper deduction, the relaxation curve can be obtained. Figure 5 The rectangular coordinate (x, y) equation of any point C in the coordinate system is:

[0165]

[0166] Expanding cosτ and sinτ in equations (1-14) and (1-15) in series, we can obtain the series expansions of x and y as follows:

[0167]

[0168] According to the coordinates of point ZH, the coordinates of point HY can be calculated in combination with the curve deflection, such as Figure 6 As shown:

[0169] Let l = l0, and the local coordinates of the end point of the transition curve, that is, point HY, can be calculated according to equations (1-16) and (1-17): Then calculate the geodetic coordinates and azimuth of point HY according to the following formula, that is, the mileage of the slow circle point within the i-th intersection range coordinate Tangent azimuth The calculation is as follows:

[0170]

[0171] Where: —The straight-line distance between the i-th circular slow point HY and the straight slow point ZH; —The rectangular coordinates of the i-th HY point in the coordinate system with ZH as the origin; —the tangent azimuth at the i-th HY point; —Coordinates of the i-th HY point; ±—the curve deviates to the left and takes -, and to the right and takes +;

[0172] The calculation of HY point is similar to the above calculation, except that the origin of the local coordinates of the transition curve is changed from ZH to HZ. You only need to calculate the coordinates and azimuth of YH in the local coordinate system first, and then convert it to geodetic coordinates, that is, the mileage of the transition circle point within the i-th intersection range. coordinate Tangent azimuth The calculation is as follows:

[0173]

[0174] Where: —The straight-line distance between the i-th circular slow point YH and the slow straight point HZ; —The rectangular coordinates of the i-th YH point in the coordinate system with HZ as the origin; —the tangent azimuth at the i-th YH point; —Coordinates of the i-th YH point; ±—If the curve deviates to the left, take -; if it deviates to the right, take +.

[0175] While coordinates can accurately represent a location, the number of digits in a coordinate system is too long, making information recording and transmission extremely inconvenient. In linear projects such as railways, highways, and pipelines, a location is often represented by a "field mileage" such as AK123+456. The "AK" in this mileage is called a prefix. Different prefixes are commonly used at different design stages. For example, AK is commonly used in the feasibility study phase, CK in the preliminary design phase, DK in the final measurement phase, and K is typically used for mileage measurements taken after the project's completion.

[0176] The "K" in AK123+456 stands for kilometer. The 123 between the "K" and the "+" represents 123 kilometers, and the 456 after the "+" represents the remainder. AK123+456 indicates that the line length from this point to the starting point AK0+000 is 123,456 meters, assuming there are no breaks in the line.

[0177] A chain break is a sudden change in mileage. There are many reasons for a chain break. For example, a railway is hundreds of kilometers long and is usually broken down into multiple sections for parallel design. The starting mileage of the first section is AK0+000, but before the design of the first section is completed, the exact starting point of the second section is unknown. In order to achieve multi-person parallel design, the starting mileage of the second section is usually estimated. For example, if it is AK92+000, Figure 7 As shown in (a), the second designer uses this mileage as the starting point to carry out the design work.

[0178] When the first designer completes their design, the final mileage often won't be exactly equal to AK92+000. The design might be shorter than expected, at AK91+500, or longer, at AK92+100. To adjust the mileage at this point, the second designer's drawings and tables, all based on AK92+000, would need to be revised, a massive undertaking. To address this, the designer creates a broken link at this junction: "AK91+950 = AK92+000," or "AK92+100 = AK92+000." This indicates that past this point, the starting mileage of the new segment will be AK92+000, allowing all design results for the second segment to remain unchanged. The left side of the equal sign in the broken link is the mileage before the break, and the right side is the mileage after the break. The mileage before the break minus the mileage after the break is the length of the broken link.

[0179] Due to the existence of a broken chain, the mileage number on site will no longer be the geometric length from this point to the starting point. For example, when a broken chain occurs, "AK91+950=AK92+000", it means that the mileage changes from AK91+950 to AK92+000, which is equivalent to shortening 50 meters. At this time, the actual distance from AK92+200 to the starting point is not 92200, but 92150. This kind of broken chain with a smaller mileage before the break than after the break is called a "short chain". Figure 7 (b) shown.

[0180] A "long chain" is a broken chain where the mileage before the break is greater than the mileage after the break, for example, "AK92+100=AK92+000". The line mileage suddenly changes from AK92+100 back to AK92+000. At this time, the actual geometric length from AK92+200 to the starting point is 92300, which is 100 meters longer than the on-site mileage of 92200. The emergence of long chains will cause "ambiguity" in mileage. For example, AK92+050 has two positions, which may be 50 meters towards the starting point from the broken point, or 50 meters towards the end point. In order to ensure the uniqueness of the mileage, the long chain must change the prefix number, for example, change the prefix number of the mileage after the break to "A1K", such as Figure 7 (c) shown.

[0181] In addition to segmented design, other common reasons for chain breaks include adjustment plans, second-line detours, etc. Line selection and design cannot be completed in one go and requires repeated comparisons and modifications. Figure 8 As shown in the figure, the initial design was partially modified, resulting in a longer route. Without adding a chain break, all mileage from the end point of the partial modification would need to be reconstructed, which would be a tremendous amount of work. However, a simple chain break cleverly solves this problem.

[0182] By adopting the above method, the mileage of the main point can be expressed, and the line mileage of the entire baseline can be expressed, which makes the coordinate expression simpler and is conducive to parallel design.

[0183] S5. Based on the correspondence between the coordinates of the main point and the mileage, the coordinates of other mileages on the baseline and the corresponding mileages are calculated to form the correspondence between all mileages and coordinates of the baseline. The digital construction of the horizontal alignment of the railway line baseline is completed.

[0184] Based on the correspondence between the coordinates of the principal point and the mileage, calculate the coordinates of other mileages on the baseline and their corresponding mileages. The steps are as follows:

[0185] Given any point on the baseline, compare the mileage with the previously calculated main point mileage to determine the line element on which the point is located, and perform calculations based on the line element:

[0186] (1) Figure 9 As shown, when the line element where the point is located is on the straight line element: the mileage of any point P on the straight line element is K P , according to the starting point HZ of the straight line i-1 and the corresponding azimuth angle A i Calculate the coordinates of point P. The calculation steps are as follows:

[0187]

[0188] Where: ΔK is the mileage difference between point P and point HZ within the range of the i-1th intersection; X P 、Y P —Latitude and longitude coordinates of point P; —The latitude and longitude coordinates of HZ within the i-1th intersection; A i —the azimuth between the i-1th and i-th intersection points;

[0189] (2) Figure 10 As shown, when the line element of the point is located on the circular curve line element: within the i-th intersection range, any point P on the circular curve line element has a mileage of K P , first calculate the distance from point P to the beginning of the circular curve HY i The arc length ΔK of point P is calculated, and the chord tangent angle α at point P is obtained. 弦切 and the chord length from P to the beginning of the circular curve The calculation method is as follows:

[0190]

[0191] Where: —The mileage from the i-th intersection point to the beginning of the circular curve, that is, the mileage of point HY; ΔK—the distance from the calculation point P to the beginning of the circular curve HY i Arc length of a point; R i —radius of the circular curve at the i-th intersection point; α 弦切 , Φ—chord tangent angle and central angle at point P; —The length of the chord from P to the beginning of the circular curve;

[0192] Finally calculate the latitude and longitude coordinates of point P (X P ,Y P ) and tangent azimuth angle α P :

[0193]

[0194] Where: —Latitude and longitude coordinates of the starting point of the circular curve; —the tangent azimuth at the beginning of the circular curve; α P - tangent azimuth at any point P on the circular curve; ± - right turn is +, left turn is -;

[0195] Among them, the coordinates of the midpoint QZ of the circular curve element are also calculated by formulas (1-24) to (1-29).

[0196] (3) When the line element where the point is located is located on the transition curve line element, determine whether the point is located on the front transition curve line element or the back transition curve line element in front of the circular curve line element;

[0197] 1) When point P is on the front transition curve element, the calculation method is as follows:

[0198]

[0199] Where: - the latitude and longitude coordinates of the ZH point of the front transition curve element; L P - Calculation points P to ZH o The length of the point; x P ,y P —The coordinates of point P in the rectangular coordinate system of the transition curve element are calculated according to formulas (1-16) and (1-17); α P - tangent azimuth at any point P on the front transition curve element; -ZH i The tangent azimuth at the point; ±—the curve deviates to the left and takes -, and right takes +;

[0200] 2) When point P is on the post-transition curve, the calculation method is as follows:

[0201]

[0202] Where: - Latitude and longitude coordinates of the HZ point of the post-transition curve element; L P - Calculation point P to HZ i The length of the point; x P ,y P —The coordinates of point P in the rectangular coordinate system of the transition curve element are calculated according to formulas (1-16) and (1-17); α P - tangent azimuth at any point P on the post-transition curve; -HZ i The tangent azimuth at the point; ±—+ for left deviation of the curve, - for right deviation.

[0203] In some embodiments, a railway line includes not only a baseline but also a secondary line. Double-track railway design typically begins with determining the baseline, and then determining the secondary line with reference to the baseline. Therefore, secondary line design is a process based on relative relationship alignment. For example, when designing the secondary line of a newly constructed double-track railway, the entire line needs to be aligned with the baseline, with the alignment defined by the parallel and winding relationships relative to the baseline. To address this issue, a reference relationship linear model was proposed, based on a systematic analysis of the various relative relationships between the secondary line and the baseline. This linear model's parameter input conforms to design practices, enabling rapid calculation of spatial alignment and mileage. Furthermore, the entire line is continuous, eliminating the need for tedious segmentation.

[0204] A characteristic of second-line plan design is that its geometry depends on the baseline. Design requirements dictate that some sections of the second line run completely parallel to the baseline, others require varying spacing and switching sides, and still others require detours, creating a complex and ever-changing situation. To establish a concise second-line alignment model, it's first necessary to identify the fundamental principles underlying the complex reference relationship between the second line and the baseline, thereby accurately describing the second line's planar alignment.

[0205] Through the analysis and research of a large number of actual line plans, it is found that the boundaries of various reference relationship sections are set on the straight line, with the intersection as the basic unit. The two-line plane line shape can be expressed by giving the reference relationship of the two-line intersection relative to the baseline intersection.

[0206] Therefore, in step S5, after forming the correspondence between all the mileages and coordinates of the baseline, the second line construction step is also included:

[0207] With reference to the baseline, the parallel or winding relationship of the second line relative to the baseline is given. Through the line section reference relationship matrix and the intersection reference relationship matrix, the mileage and coordinate relationship of the second line are calculated, and the digital construction of the railway line plane alignment is completed.

[0208] In the construction of the second line, the reference relationship between the intersection of the second line and the intersection of the baseline is divided into two categories: parallel and detour. The intersection types of the parallel line include: parallel and parallel intersection, parallel and non-parallel intersection, intersection before the S-bend, and intersection after the S-bend; the detour intersection types include: detour starting intersection, detour middle intersection, detour ending intersection, and single detour intersection.

[0209] (1) When the reference relationship between the intersection of the two lines and the intersection of the baseline is parallel:

[0210] like Figure 11 As shown, the front and rear straight lines of the intersection point JD' are parallel to the front and rear straight lines of the corresponding intersection point JD of the baseline. This kind of intersection reference relationship can be expressed by the following vectors:

[0211] JD'=[TJD',RJD',D Q ,D H ,R',l'0] T ; (2-1)

[0212] Among them, TJD' is the intersection type; RJD' is the intersection number of the second line corresponding to the baseline reference line; D Q and D H The line spacing between the front tangent edge and the back tangent edge, that is, the front line spacing D Q , back line spacing D H ; R' and l'0 are the radius and the slow length of the second line at the JD' point respectively; T represents the transpose;

[0213] It should be noted that when the front line spacing and the back line spacing of the intersection satisfy the relationship D Q =D H When the radius is determined by the concentric circle rule, the selection of the transition length usually needs to consider the inward displacement of the transition curve to meet the requirements of widening the curve line spacing.

[0214] For parallel parallel intersections, such as Figure 12 As shown, A, JD i , B and JD' i It can form a parallelogram. It is stipulated that when the current intersection point is on the left side of its reference line, D' Qi and D' Hi When it is negative and on the right side, D' Qi and D' Hi Is positive, the second line deflection angle α when the curve turns left i is negative, right turns positive, α i Refers to the deflection angle of a certain intersection point of the two lines, then according to Figure 12 The following JD' can be derived i Coordinate calculation formula:

[0215]

[0216]

[0217] Where: X i ,Y i -JD i The latitude and longitude coordinates of i ,Y′ i -JD′ i The latitude and longitude coordinates of fwj i ' Q ,fwj i ' H - the azimuth angles of the front and back tangent edges of the curve; α i —Deflection angle of the second line curve; BJD′ i ,BJD i - respectively, the edges BJD′ i and BJD i length.

[0218] (2) When the reference relationship between the intersection of the two lines and the intersection of the baseline is a parallel but non-parallel intersection:

[0219] In some parallel sections, the line connecting the intersection of two lines is not parallel to the line connecting the corresponding baseline intersection points. However, the line spacing is small, and the two lines share structures below the line, so it does not constitute a detour. This is called a "parallel but not parallel section." The intersection point in this section is called a "parallel but not parallel intersection point." This type of intersection data can be represented by the following vector:

[0220] JD'=[TJD',RJD',X 二线 ,Y 二线 ,R',l'0] T ; (2-3)

[0221] where X 二线 , Y 二线 Indicates the absolute coordinates of the intersection, that is, the intersection latitude X 二线 and the intersection distance Y 二线 ; TJD' is the intersection type, RJD' is the intersection number of the second line corresponding to the baseline reference line; R' and l'0 are the radius and the length of the second line at the JD' point respectively.

[0222] (3) When the reference relationship between the intersection of the two lines and the intersection of the baseline is the intersection before the bend and the intersection after the bend:

[0223] When the line spacing needs to be changed on a straight line section of the baseline, it is usually achieved by setting a pair of reverse curves with the same radius, ramp length and turning angle on the second line. Designers usually call such reverse curves "S-bends". Figure 13 As shown, the intersection point JD' Q 、JD' H They are the front intersection point and the rear intersection point of the S-bend respectively.

[0224] When designers design an S-bend, they are usually unable to directly give the absolute coordinates of the two intersection points. They need to calculate the S-bend intersection parameters according to the requirements. There are generally two types of S-bend solutions:

[0225] 1) Given the line spacing D before the S-bend distance change Q The line spacing D after the S-bend distance change H , the entire S-curve starting mileage and the minimum straight line length L in the middle min , achieving the shortest distance change. At this time, the intersection point before and after the S-bend can be represented by the following two vectors:

[0226]

[0227] JD' H =[TJD',RJD',D H ,L min ,R' H ,l'0] T ; (2-4)

[0228] When formula (2-4) is used to represent the S-bend intersection, the intersection coordinate solution process is as follows:

[0229] ① Solve the deflection angle α of the second line curve

[0230] JD' Q The tangent length T' Q and JD' H The tangent length T' H The calculation formula is as follows:

[0231]

[0232] Among them, m' and P' are the tangent perpendicular distance of the two lines and the inward displacement of the circular curve respectively.

[0233] ②The length of the straight line is L min , then in triangle JD' Q P JD' H (like Figure 13 ) has the following relationship:

[0234] (T' Q +T' H +Lmin )sinα=D H -D Q ; (2-6)

[0235] The deflection angle α can be solved by combining formulas (2-5) and (2-6).

[0236] ③Basis Calculate ZH′ on the reference line Q Coordinates ZH' can be calculated using the following formula Q coordinate

[0237]

[0238] Where: fwj—azimuth of the straight side of the reference line; ±—the second line takes + on the right side of the baseline and - on the left side.

[0239] ④ Calculate JD' according to the following formula Q coordinate

[0240]

[0241] ⑤JD' H The coordinates can be calculated by the following formula

[0242]

[0243] In the formula: ±—For the second-line S-bend, take + if it deviates to the right and take - if it deviates to the left.

[0244] 2) Given the line spacing D before and after the S-bend change Q 、D H , the projected mileage of the start and end points of the entire S-curve The S-bend is solved. At this point, the intersection points before and after the S-bend can be expressed as:

[0245]

[0246] When the S-bend intersection is expressed in the form of formula (2-10), the intersection coordinate solution process is as follows:

[0247] ① Solve the curve deflection angle α

[0248] The starting and ending mileages of the entire curve are Virtual triangle JD' on the second line Q PJD' H (like Figure 13 ) has the following relationship:

[0249]

[0250] The deflection angle α can be solved by combining formulas (2-5) and (2-11).

[0251] ②Basis Calculate the corresponding reference line ZH′ Q ,HZ′ H Coordinates

[0252] Calculate ZH according to formula (2-7) Q Point coordinates And calculate HZ according to the following formula H :

[0253]

[0254] In the formula: ±—the second line takes + on the right side of the baseline and - on the left side.

[0255] It is worth noting that the S-curve belongs to the parallel section, and the mileage of any point on it is determined by the projected mileage of the corresponding reference line. Therefore:

[0256]

[0257] (4) When the reference relationship between the intersection of the second line and the intersection of the baseline is the detour starting intersection, intermediate intersection or end intersection:

[0258] like Figure 14 A typical detour section with multiple intersections is shown. The first intersection of the detour section is JD i 'For the detour starting intersection and the last intersection JD i+3 'For the detour end intersection, the middle part JD i+1 ', JD i+2 ' is the middle intersection point of the detour. The front clipping line edge of the starting intersection point of the detour section is parallel to the corresponding baseline clipping line edge. During the design process, designers can usually easily give the line spacing D of the front clipping line. Q The projected mileage K of the detour starting point on the baseline JD And radius, slow length.

[0259] Therefore, the intersection point can be expressed as:

[0260] JD'=[TJD',RJD',D Q ,K JD ,R',l'0] T ; (2-14)

[0261] The back clip line around the ending intersection is parallel to the corresponding clip line edge of the baseline, and the line spacing is D Q . Similar to the detour starting intersection, it can be expressed as:

[0262] JD'=[TJD',RJD',DH ,K JD ,R',l'0] T ; (2-15)

[0263] The intersection point of the detour is relatively free and is not constrained by the baseline. Designers can directly specify the absolute coordinates, radius, and length of the intersection point when designing. This type of intersection point can be expressed as:

[0264] JD'=[TJD',RJD',X 二线 ,Y 二线 ,R',l'0] T ; (2-16)

[0265] For the calculation of the coordinates of the detour starting and ending intersection points, the reference line straight edge azimuth fwj can be obtained according to the intersection index RJD' of the reference line, and the projection mileage K JD The coordinates of the projection point of the intersection point on the reference line can be determined [X JD’ , Y JD’ ] T , the distance between the front and rear straight lines is D, then the intersection coordinates [X JD’ ,Y JD’ ] T It can be calculated as follows:

[0266]

[0267] Where: —Coordinates of the starting and ending intersection points of the orbit; —Coordinates of the projection points of the detour’s starting and ending intersection points on the reference line; Q ,fwj H —Azimuth of the straight line edge of the reference line at the starting and ending intersection points of the detour; ±—the second line takes + on the right side of the baseline and - on the left side.

[0268] (5) When the reference relationship between the second line intersection point and the baseline intersection point is a single detour intersection point:

[0269] like Figure 15 As shown, there is only one intersection point JD' in the detour section, which is defined as a single detour intersection point. The front and rear straight lines of this type of intersection must be parallel to the corresponding intersection point of the baseline. The front and rear line spacing D is given during design. Q , D H And radius, slow length. Such intersection can be expressed as:

[0270] JD'=[TJD',RJF',D Q ,D H ,R',l'0] T ; (2-19)

[0271] Based on the above-mentioned various intersection relationships, all types of intersection data can be represented by the following unified six-dimensional vector:

[0272] JD'=[TJD',RJD',U,V,T',l'0] T ; (2-20)

[0273] Among them, U and V corresponding to various intersection points are shown in Table 1:

[0274] Table 1 Meaning of various types of intersection points U and V

[0275]

[0276] By combining all the intersection column vectors in the order of increasing mileage, we can obtain the reference relationship matrix of the intersection points of the entire line as follows:

[0277]

[0278] From the perspective of underground structure design and mileage calculation, the relationship between a designed secondary line and its reference baseline can be categorized as parallel or bypass. In parallel sections, the secondary line is closely spaced from the baseline, sharing subsurface structures such as the roadbed, bridges, and tunnels. The secondary line's mileage is also projected from the baseline. In bypass sections, the secondary line is spaced farther from the baseline, possessing its own roadbed, bridges, tunnels, and other structures. The secondary line also has completely independent mileage. The parallel and bypass reference relationships between secondary lines and their reference baselines can be represented by the following segment reference relationship vector r:

[0279] r=[T',K S ,K E ,JD S ,JD E ] T ; (2-22)

[0280] Where T is the section reference relationship type, including parallel and detour, K S , K E JD is the starting and ending mileage of the section. S , JD E Number the starting and ending intersection points of the section.

[0281] The entire second line is connected by staggered parallel and bypass sections. m After sorting by mileage and then combining, a matrix M reflecting the reference relationship of the route can be formed. R '.

[0282]

[0283] Since the number of intersections in each parallel and detour section is quite different, in order to avoid the matrix M R 'There are a lot of useless "0" elements in the line section reference relationship matrix M R ' only records the start and end intersection numbers, and the specific intersection data is recorded in the intersection reference relationship matrix M RJD '(see formula 2-21). Combined with M R ' and M RJD 'A reference linear model can be established to calculate the geometric parameters and mileage of the line.

[0284] After the second-line model is constructed, the model is solved:

[0285] Route design requires determining the spatial shape and position of any point along the entire route, and being able to quickly and easily convert and calculate the mileage coordinates of any point.

[0286] Solving the model involves the following steps:

[0287] (1) Geometric shape calculation

[0288] By determining the coordinates, radius, and ramp length of all intersection points on the line plane, the spatial geometry of the line can be determined based on the existing model algorithm. The data required to solve the spatial geometry is the intersection data matrix M as follows: JD :

[0289]

[0290] Line intersection reference relationship matrix M RJD In the equation, the absolute coordinates, radius, and slow length of the middle intersection point of the detour section and the parallel and non-parallel intersection point are all given by the designer and can be directly put into the above matrix. The coordinates of the parallel and parallel intersection points, the starting and ending intersection points of the S-bend, and the starting and ending intersection points of the detour can be known from the establishment of the model.

[0291] When the intersection data matrix M JD After it is fully determined, the coordinates of each intersection point can be quickly solved, and then the line can be decomposed into various plane linear units (straight lines, transition curves, circular curves) to realize geometric line position calculation.

[0292] (2) Determine the starting and ending points of the merge and detour sections

[0293] The starting and ending mileage K of the combined and detour sections in the section reference relationship column vector S ,K E It can be specified by the designer during the design process, or it can be automatically determined by the computer according to the following principles:

[0294] (1)K S ,K E They are all located on the straight line between the baseline and the second line;

[0295] (2)K S ,K E It should be located at the position of the whole hundred meters as much as possible. If there is no whole hundred-meter mark on the straight line, it should be located at the position of the whole ten meters. If there is no ten-meter mark, it should be set at the whole meter. In special circumstances, it may not be rounded up.

[0296] For the entire second line, the merging and detour sections are connected end to end and appear in an interlaced manner. It is only necessary to determine the starting and ending mileage of each detour section to determine all the K S ,K E .like Figure 16 As shown, the detour starting point mileage K S The determination algorithm is as follows:

[0297] ① Take out the first intersection point JD of the detour section S , calculate the ZH coordinates of the intersection

[0298] ②Calculation Projected mileage K on the baseline ZH ;

[0299] ③ Take out JD S Corresponding baseline reference intersection point RJD S , and calculate the mileage of the intersection ZH point

[0300] ④Set K S Initial value of K′ S It is the minimum mileage point that is located on both the baseline and the second line clamp straight line;

[0301] ⑤ On the straight line, make a line K′ S Round down to the nearest hundred meters to get K S If it is impossible to round to 100 meters, round to 10 meters or meters.

[0302] ⑥In K S A detour link is set up.

[0303] Detour end point K E The determination method is similar to this, using JD E and its corresponding baseline intersection point RJD E The HZ point is projected and the mileage is rounded up.

[0304] The detour section requires the construction of independent single-track subgrades, bridges, tunnels and other structures, which no longer share the mileage with the baseline. A separate mileage system needs to be set up. After the detour section ends, the second line and the baseline share the same structure again, and the mileage of the baseline needs to be used again. Therefore, a pair of broken links need to be set at the starting and ending points of the detour section. Figure 17As shown, the right line is the second-line route. It detours at AK78+600, creating a broken link: AK78+600 = A1K78+600. From this point on, a local mileage system is adopted, starting at A1K78+600. After the second line detours 9440.42 meters, the detour section ends at A1K88+040.42, and it then runs parallel to the baseline, requiring the projected mileage of the baseline. The mileage projected onto the baseline at A1K88+040.4 is AK87+500, requiring a broken link: A1K88+040.42 = AK87+500.

[0305] (3) Conversion between mileage and coordinates

[0306] Unlike the baseline, the mileage of points on secondary railway lines is related to reference relationships. A detour section is equivalent to a localized single line, and the baseline calculation model can be used to calculate mileage. However, for points in parallel sections, which share structures such as roadbeds, bridges, and tunnels with the baseline, the mileage should be calculated based on the projected mileage of the reference baseline, in accordance with Chinese design practices. The reference linear model fully considers the reference relationships between lines, allowing for quick and convenient conversion between mileage and coordinates.

[0307] 1. The coordinate conversion mileage process is as follows:

[0308] ① According to the coordinates, radius, and geometric parameters of the intersection of the two lines, calculate the geometric length from the coordinate point to the starting point of the line;

[0309] ② According to the starting and ending mileages of the section in the line reference relationship matrix, determine the reference relationship section where the geometric mileage is located;

[0310] ③ If the local reference relationship is parallel segment transfer ④, otherwise it is bypass segment transfer ⑤;

[0311] ④ Such as Figure 18 As shown, project point P1 on the parallel segment onto the baseline and take the mileage of the projected point P1′ on the baseline as AK78+000;

[0312] ⑤ Treat the detour section as a separate baseline to calculate its mileage. The distance between point P2 on the detour section and the starting point A1K78+600 is 1000m, so its mileage is A1K79+600.

[0313] 2. The basic process of mileage coordinate conversion is as follows:

[0314] ① Calculate the continuous mileage of the point based on the broken link data of the second-line line;

[0315] ② According to the starting and ending mileage of the section in the reference relationship matrix of the second-line route, determine the reference relationship section where the mileage is located;

[0316] ③ If the reference relationship is parallel segment transfer ④, otherwise it is bypass segment transfer ⑤;

[0317] ④ Calculate the mileage point P1′ on the baseline, draw a perpendicular line through P1′ to the baseline, and the coordinates of the intersection of the perpendicular line and the second line P1 are the coordinates you need;

[0318] ⑤ Treat the detour segment as a separate baseline. Subtract the mileage of the detour segment's starting point from the mileage of P2 to obtain the geometric distance from the detour segment's starting point. Calculate its coordinates based on this geometric distance (refer to Section 1.3).

[0319] The method for digitally constructing the railway line plane alignment described in this embodiment has the following advantages:

[0320] 1) A systematic theoretical study on the digital model of railway line plane alignment was carried out, enriching the theory of railway line design.

[0321] 2) This invention achieves high-precision calculation of the spatial position of railway line alignments, applicable to both single- and double-track railways. It provides a theoretical basis for digital design, construction, and operation and maintenance of railway lines, and offers technical support for the implementation of "intelligent railway construction" in my country.

[0322] 3) Utilizing this invention's digitalized line model, a series of digital and intelligent railway line software has been developed. These results have been applied to major railway projects both domestically and internationally, achieving significant social and economic benefits. This has enabled the transformation of my country's railway line design from manual design to digital design and then to intelligent design, improving the quality of my country's railway line design.

[0323] Example 2

[0324] A system for digitally constructing a railway line's plane alignment includes at least one processor and a memory communicatively connected to the at least one processor; the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute a method for digitally constructing a railway line's plane alignment as described in Example 1.

[0325] Example 3

[0326] A computer-readable medium stores instructions executable by a processor, wherein when the instructions are executed by the processor, the processor executes a method for digitally constructing the plane alignment of a railway line as described in Example 1.

[0327] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for digitally constructing the plane alignment of a railway line, characterized by: Include the build steps for the baseline: S1. Divide the baseline into a number of straight line elements and two continuous curve line elements connecting two adjacent straight line elements. The curve line elements include circular curve line elements and transition curve line elements connecting the two ends of the circular curve line element. Each curve line element has a corresponding intersection point. S2. Calculate the curve length and tangent length of each curve element based on the coordinates of each intersection point, the radius of the circular curve element, and the length of the transition curve element; S3. Calculate the main point mileage based on the baseline's starting mileage K0, the distance D1 between the first intersection point JD1 and the baseline's starting mileage K0, the coordinates of each intersection point, the length of each transition curve element, and the curve length and tangent length of each curve element. The main point mileage includes the straight-to-slow point mileage, the transition curve point mileage, the midpoint mileage, the transition curve point mileage, and the transition straight point mileage. The straight-to-slow point mileage is the mileage of the boundary between a straight line element and a transition curve element in the direction of the route. The transition curve point mileage is the mileage of the starting end of a circular curve element. The midpoint mileage is the mileage of the midpoint of a circular curve element. The transition curve point mileage is the mileage of the end of a circular curve element. The transition straight point mileage is the mileage of the boundary between a transition curve element and a straight line element in the direction of the route. S4. Calculate the coordinates and tangent azimuth of the principal point based on the latitude and longitude coordinates of each intersection point, the radius of the curve element, the tangent length, and the azimuth of the front tangent line, and obtain the corresponding relationship between the coordinates of the principal point and the mileage; S5. Based on the correspondence between the coordinates of the main point and the mileage, the coordinates of other mileages on the baseline and the corresponding mileages are calculated to form the correspondence between all mileages and coordinates of the baseline. The digital construction of the horizontal alignment of the railway line baseline is completed.

2. The method for digitally constructing the plane alignment of a railway line according to claim 1, characterized in that: In step S2, the steps of calculating the curve length and tangent length of each curve element according to the coordinates of each intersection point, the radius of the circular curve element, and the length of the transition curve element are as follows: Calculate the deflection angle α of the curve element of the current curve line element through the coordinates of the current intersection point, the previous intersection point and the next intersection point; The transition curve element angle β0 of the curve element is calculated based on the transition curve element length l0 of the current curve element and the radius R of the circular curve element. The calculation formula is: The tangent-vertical distance m and the inward displacement p of the transition curve element are calculated based on the transition curve element length l0, the circular curve element radius R and the transition curve element rotation angle β0 of the current curve element. The calculation formula is: The tangent length T of the current curve element is calculated based on the circular curve element radius R, inward displacement p, deflection angle α and tangent-vertical distance m of the current curve element. The calculation formula is: The curve length L of the current curve element is calculated based on the circular curve element radius R, the deflection angle α and the length l0 of the transition curve element. The calculation formula is:

3. The method for digitally constructing the plane alignment of a railway line according to claim 1, characterized in that: The steps to calculate the main point mileage are as follows: According to the starting mileage K0 of the baseline, the distance D1 between the first intersection point JD1 and the starting mileage K0 of the baseline, the tangent length T1 of the curve element corresponding to the first intersection point JD1, and the length l of the curve element 01 and the curve length L1, the plane distance D between the i-th and i-1-th intersection points i The tangent length T of the curve element corresponding to the i-th intersection point i , curve element length l 0i and curve length L i Calculate the mileage of the first straight-line point Slow dot mileage Mileage at the midpoint Round trip mileage Gentle straight mileage and the mileage of the i-th straight slow point Slow dot mileage Mileage at the midpoint Round trip mileage Gentle straight mileage i>

1.

4. The method for digitally constructing the plane alignment of a railway line according to claim 3, characterized in that: Calculate the first straight-slow point mileage based on the starting mileage K0 of the baseline, the distance D1 between the first intersection point JD1 and the starting mileage K0 of the baseline, and the tangent length T1 of the curve element corresponding to the first intersection point JD1. The calculation formula is as follows: According to the plane distance D between the i-th and i-1-th intersection points o , the tangent length T of the curve element corresponding to the i-1th intersection point i-1 The tangent length T of the curve element corresponding to the i-th intersection point i Calculate the length of the front straight line of the i-th intersection i>1; According to the straightening point of the curve element corresponding to the previous intersection point The length of the straight line before the i-th intersection point Calculate the mileage of the i-th straight-slow point According to the mileage of the i-th straight slow point and the curve element length l 0i Calculate the mileage of the i-th slow circle point According to the mileage of the i-th slow circle point and curve length L i Calculate the mileage of the i-th curve midpoint as half of According to the i-th midpoint Curve length L i and the curve element length l 0i Calculate the mileage of the i-th circle slow point According to the straight and slow point mileage of the curve line element corresponding to the current intersection and curve length L i Calculate the mileage of the i-th straightening point Among them, the front clip straight line length Mileage of the i-th straight-slow point Slow dot mileage Mileage at the midpoint Round trip mileage Gentle straight mileage The calculation formula is as follows:

5. The method for digitally constructing the plane alignment of a railway line according to claim 1, characterized in that: Calculating the coordinates of the principal point and the tangent azimuth includes: According to the latitude and longitude coordinates (X i ,Y i ), curve element radius R i , tangent length T i and the front tangent azimuth A i Calculate the mileage of the i-th straight-slow point Mileage of the i-th slow circle point i midpoint mileage Mileage of the i-th circle slow point and the mileage of the i-th straightening point Coordinates and tangent azimuth of Mileage of straight and slow points within the i-th intersection coordinate Tangent azimuth The calculation is as follows: Mileage of straight and slow points within the i-th intersection coordinate Tangent azimuth The calculation is as follows: Mileage of the slow circle point within the i-th intersection coordinate Tangent azimuth The calculation is as follows: Where: —The straight-line distance between the circular slow point HY and the straight slow point ZH; —The rectangular coordinate of point HY in the coordinate system with point ZH as the origin; —Tangent azimuth at point HY; —H-Y point coordinates; ±—the curve is - for left deviation and + for right deviation; Mileage of the slow circle point within the i-th intersection coordinate Tangent azimuth The calculation is as follows: Where: —The straight-line distance between the circular slow point YH and the straight-line slow point HZ; —The rectangular coordinate of point YH in the coordinate system with point HZ as the origin; —Tangent azimuth at point YH; —YH point coordinates; ±—If the curve deviates to the left, take -; if it deviates to the right, take +.

6. The method for digitally constructing the plane alignment of a railway line according to claim 1, characterized in that: Based on the correspondence between the coordinates of the principal point and the mileage, calculate the coordinates of other mileages on the baseline and their corresponding mileages. The steps are as follows: Given any point on the baseline, compare the mileage with the previously calculated main point mileage to determine the line element on which the point is located, and perform calculations based on the line element: (1) When the line element where the point is located is on the straight line element: the mileage of any point P on the straight line element is K P , according to the starting point HZ of the straight line i-1 and the corresponding azimuth angle A i Calculate the coordinates of point P. The calculation steps are as follows: Where: ΔK is the mileage difference between point P and point HZ within the range of the i-1th intersection; X P 、Y P —Latitude and longitude coordinates of point P; —The latitude and longitude coordinates of HZ within the i-1th intersection; A i —the azimuth between the i-1th and i-th intersection points; (2) When the line element of the point is located on the circular curve line element: within the i-th intersection range, any point P on the circular curve line element has a mileage of K P , first calculate the distance from point P to the beginning of the circular curve HY i The arc length ΔK of point P is calculated, and then the chord angle α at point P and the chord length from P to the beginning of the circular curve are calculated. The calculation method is as follows: Where: —The mileage of the starting point of the circular curve, that is, the mileage of point HY; ΔK—the distance from the calculation point P to the starting point HY of the circular curve i Arc length of a point; R i — radius of the circular curve; α, Φ — chord tangent angle and central angle at point P; —The length of the chord from P to the beginning of the circular curve; Finally calculate the latitude and longitude coordinates of point P (X P ,Y P ) and tangent azimuth angle α P : Where: —Latitude and longitude coordinates of the starting point of the circular curve; —the tangent azimuth at the beginning of the circular curve; α P - tangent azimuth at any point P on the circular curve; ± - right turn is +, left turn is -; (3) When the line element where the point is located is located on the transition curve line element, determine whether the point is located on the front transition curve line element or the back transition curve line element in front of the circular curve line element; 1) When point P is on the front transition curve element, the calculation method is as follows: Where: - The latitude and longitude coordinates of the ZH point of the front transition curve element; L P - Calculation points P to ZH i The length of the point; x P ,y P —The coordinates of point P in the rectangular coordinate system of the transition curve element; α P - tangent azimuth at any point P on the front transition curve element; -ZH i The tangent azimuth at the point; ±—the curve deviates to the left and takes -, and right takes +; 2) When point P is on the post-transition curve, the calculation method is as follows: Where: - Latitude and longitude coordinates of the HZ point of the post-transition curve element; L P - Calculation point P to HZ i The length of the point; x P ,y P —The coordinates of point P in the rectangular coordinate system of the transition curve element: α P - tangent azimuth at any point P on the post-transition curve; -HZ i The tangent azimuth at the point; ±—+ for left deviation of the curve, - for right deviation.

7. The method for digitally constructing the plane alignment of a railway line according to claim 1, characterized in that: In step S5, after the correspondence between all the mileages and coordinates of the baseline is formed, the second line construction step is also included: With reference to the baseline, the parallel or winding relationship of the second line relative to the baseline is given. Through the line section reference relationship matrix and the intersection reference relationship matrix, the mileage and coordinate relationship of the second line are calculated, and the digital construction of the railway line plane alignment is completed.

8. The method for digitally constructing the plane alignment of a railway line according to claim 7, characterized in that: In the construction of the second line, the reference relationship between the intersection of the second line and the intersection of the baseline is divided into two categories: parallel and detour. The intersection types of the parallel line include: parallel and parallel intersection, parallel and non-parallel intersection, S-bend intersection before and S-bend intersection; the detour intersection types include: detour starting intersection, detour middle intersection, detour ending intersection, and single detour intersection. All types of intersection data can be represented by the following unified six-dimensional vector: JD'=[TJD',RJD',U,V,R',l'0] T (2-20) Among them, U and V corresponding to various intersection points are shown in Table 1: By combining all the intersection column vectors in the order of increasing mileage, we can obtain the reference relationship matrix of the intersection points of the entire second-line route as follows: The parallel and bypass reference relationship of the second-line reference baseline can be expressed by the following segment reference relationship vector r: r=[T’,K S ,K E ,JD S ,JD E ] T ; (2-22) Where T' is the section reference relationship type, including parallel and detour, K S , K E JD is the starting and ending mileage of the section. S , JD E Number the starting and ending intersection points of the section; The entire second line is connected by staggered parallel and detour sections, and all local reference relationship vectors r1, r2, ..., r m After sorting by mileage and then combining, a matrix M reflecting the reference relationship of the route can be formed. R '; Combined with M R ' and M RJD 'A reference linear model can be established to calculate the geometric parameters and mileage of the second-line line.

9. A railway line plane alignment digital construction system, characterized by: The invention comprises at least one processor and a memory in communication with the at least one processor; the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute a method for digitally constructing a plane alignment of a railway line according to any one of claims 1 to 8.

10. A computer-readable medium, characterized in that Instructions executable by a processor are stored thereon, and when the instructions are executed by the processor, the processor executes a method for digitally constructing the plane alignment of a railway line as claimed in any one of claims 1 to 8.

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