CN110232226B - Planar line shape reconstruction design method for lines on railway bridge - Google Patents

Planar line shape reconstruction design method for lines on railway bridge Download PDF

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CN110232226B
CN110232226B CN201910452019.2A CN201910452019A CN110232226B CN 110232226 B CN110232226 B CN 110232226B CN 201910452019 A CN201910452019 A CN 201910452019A CN 110232226 B CN110232226 B CN 110232226B
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蔡小培
刘万里
冯鸿雪
常文浩
侯博文
高亮
彭华
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Beijing Jiaotong University
China State Railway Group Co Ltd
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China Railway Corp
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Abstract

The invention provides a planar line shape reconstruction design method for a line on a railway bridge, which adopts a total station instrument to measure the center line coordinates of a track of the line on the railway bridge and divides straight line and curve sections in a measuring line; fitting the straight line sections to determine the slope of the straight line, and further determining the deflection angle of each curve section; and based on the deflection angle of each curve section, establishing a reconstructed curve by taking the length of the easement curve and the radius of the circular curve as variables, and optimizing by taking the dial value at the measuring point as a constraint function and taking the minimum sum of squares of the dial values as a target to obtain a reconstructed plane line shape. The method can accurately and effectively reconstruct the reasonable planar line shape of the seamless line on the bridge.

Description

Planar line shape reconstruction design method for lines on railway bridge
Technical Field
The invention relates to the field of railway engineering design, in particular to a design method for reconstructing a plane line shape of a line on a railway bridge.
Background
After the line on the railway bridge is delivered to operation, due to the complex interaction between the beam-rail and the wheel-rail and the influence of other various external forces, the center of the rail (namely the center line of the line) gradually deviates from the original designed line, the center line of the line is not smooth any more, and the driving safety is threatened in severe cases, so that the line-shaped reconstruction maintenance is required to be carried out on the line regularly.
The traditional railway reconstruction measuring and setting method mainly comprises a rope alignment method and an angle deviation method. The rope straightening method is a method for straightening curves, and the poking value of each point is calculated by utilizing the principle of an involute according to the relation between an actually measured curve right vector and a calculated curve right vector, so that the aim of rounding the curves is fulfilled; the deflection angle method is based on the principle of an involute, the difference value between the designed involute of each measuring point and the existing involute is calculated, and the difference value is the shifting distance of the measuring point. The rope straightening method and the deflection angle method have a plurality of assumptions and equivalent substitutions when applied. Operation practice shows that the two methods in the prior art are difficult to control errors, the reconstructed radius of the circular curve and the length of the easement curve have large deviation with the current situation, and the calculation workload is large. Because the high-speed railway strictly controls the track irregularity, the maintenance and repair work of the high-speed railway cannot be adapted by adopting a rope straightening method and an angle deviation method.
In recent years, reconstruction of a line plane by an absolute coordinate method has become a main maintenance method for a high-speed railway, and the method has the following operation modes: firstly, measuring the coordinates of a series of points along the center of the track; then reconstructing a line central line which is closest to the measuring points and meets the design specifications; and finally, correcting the track to the reconstruction line, wherein the shifting amount of each point is the shifting amount. In order to reduce the traffic interference to the existing railway, the sum of absolute values or the sum of squares of the expected dialing amount of an operation department is minimum. But the original design alignment is not usually the least square sum of the pitches solution. Therefore, a method for reconstructing a planar line shape of a line on a railway bridge quickly, accurately and automatically is needed.
Disclosure of Invention
The invention provides a method for reconstructing and designing the planar line shape of a line on a railway bridge, which is used for accurately and effectively reconstructing the planar line shape of a seamless line on the bridge.
In order to achieve the purpose, the invention adopts the following technical scheme.
The invention provides a design method for planar line shape reconstruction of a line on a railway bridge, which comprises the following steps:
measuring the coordinates of the center line of a track on a railway bridge by using a total station, and dividing straight line and curve sections in a measuring line;
fitting the straight line sections to determine the slope of the straight line, and further determining the deflection angle of each curve section;
and based on the deflection angle of each curve section, establishing a reconstructed curve by taking the length of the easement curve and the radius of the circular curve as variables, and optimizing by taking the dial value at the measuring point as a constraint function and taking the minimum sum of squares of the dial values as a target to obtain a reconstructed plane line shape.
Preferably, the method for measuring the center line coordinates of the track on the railway bridge by using the total station and dividing the straight line and the curve sections in the measuring line comprises the following steps: and (3) removing interference points in the measuring line by combining MATLAB programming through a method of establishing a gradient threshold, identifying straight line segments in the measuring line, segmenting the line through straight line segment coordinates, and calculating the mileage of each measuring point.
Preferably, fitting the straight line segments to determine the slope of the straight line and further determine the deviation angle of each curve segment includes: and performing function fitting on the line of the straight line section by adopting a least square method, calculating the quadrant angles of the straight lines at the two ends of the curve section, determining the respective azimuth angles by the quadrant angles so as to obtain the azimuth angle difference between the straight lines at the two ends, and determining the deflection angle of the curve section by the azimuth angle difference.
Preferably, based on the deflection angle of each curve segment, with the length of the easement curve and the radius of the circular curve as variables, a reconstruction curve is established, with the dial value at the measurement point as a constraint function, and with the sum of the squares of the dial values as a target, optimization is performed to obtain a reconstructed planar line shape, including: and writing a coordinate and dialing amount calculation formula of a reconstruction curve in the EXCEL, and obtaining a reconstructed plane line shape based on a planning solver in the EXCEL.
Preferably, based on the deflection angle of each curve section, the length of the easement curve and the radius of the circular curve are used as variables to establish a reconstruction curve, the dial value at the measuring point is used as a constraint function, and the square of the dial value is used as a square of the dial valueThe minimum sum is used as a target, optimization is carried out to obtain a reconstructed plane line shape, and the method further comprises the following steps: if the line comprises multiple straight lines and multiple curves, the length L of the straight line between two adjacent curves is usedjzAs a constraint function. The technical scheme provided by the method for designing the planar line shape reconstruction of the line on the railway bridge can be seen that the method can be applied to the planar line rectification on the bridge, has a solid theoretical basis and strict derivation calculation, and can reconstruct a reasonable line shape based on a self-contained planning solver in EXCEL by compiling a coordinate and dial calculation formula of a reconstruction curve in the EXCEL; the method has the advantages of simple operation, less calculation amount, high calculation precision and the like, meanwhile, only a calculation formula needs to be compiled once in the EXCEL, and reasonable line shapes can be reconstructed by changing the existing coordinates and setting constraint variables in the later period, so that the method is high in reusability; the reconstructed line shape has the advantages of smooth line, small track shifting amount and the like, and the method can be widely applied to the engineering department for reconstructing the planar line on the bridge.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
Fig. 1 is a flowchart of a planar line shape reconstruction design method for a line on a railway bridge according to embodiment 1;
FIG. 2 is a schematic diagram of a design principle of planar line shape reconstruction of a line on a railway bridge;
FIG. 3 is a schematic diagram of a line measurement;
FIG. 4 is a schematic view of various quadrant angles;
FIG. 5 is a schematic view of various azimuth angles;
FIG. 6 is a schematic diagram illustrating the calculation of the difference between the azimuth angles of the tangent lines on both sides of the curve;
FIG. 7 is a schematic diagram of elements of a reconstruction curve;
FIG. 8 is a schematic view of the ZH-xy coordinate system;
FIG. 9 is a schematic view of the HZ-x 'y' coordinate system;
FIG. 10 is a schematic diagram of the conversion of the HZ-x 'y' coordinate system to the ZH-xy coordinate system;
FIG. 11 is a schematic view showing the positional relationship between the measurement coordinate system and the ZH-xy coordinate system and the HZ-x 'y' coordinate system;
FIG. 12 is a schematic diagram of a circuit including a plurality of curves;
FIG. 13 is a schematic diagram illustrating the calculation of basic parameters of a circuit reconfiguration design table;
FIG. 14 is a schematic diagram of a coordinate-method alignment curve of a line reconfiguration design table;
FIG. 15 is a diagram of a line reconstruction coordinate interface;
FIG. 16 is a graphical interface for calculation of dialing amounts;
FIG. 17 is a schematic diagram of a planar reconstruction line optimization process;
FIG. 18 is a graph showing a comparison of the curvatures of the reconstructed line of example two;
fig. 19 is a graph showing a curvature comparison after line reconstruction in the third embodiment.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
As used herein, the singular forms "a", "an", "the" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.
It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
For the convenience of understanding the embodiments of the present invention, the following description will be further explained by taking several specific embodiments as examples in conjunction with the drawings, and the embodiments are not to be construed as limiting the embodiments of the present invention.
Example 1
Fig. 1 is a flowchart of a method for designing planar line shape reconstruction of a line on a railway bridge according to this embodiment, and fig. 2 is a schematic diagram of a principle of planar line shape reconstruction of a line on a railway bridge, and with reference to fig. 1 and fig. 2, the method includes:
s1, measuring the coordinates of the center line of the track on the railway bridge by using a total station, and dividing the straight line and curve sections in the measuring line.
The plane line shape of the ballast track on the bridge is mainly a simple curve, and the line adopts a combination mode of 'straight line-curve-straight line'. In the existing line plane reconstruction design on the bridge, a total station is adopted to measure the coordinates of the center line of a line track on a railway bridge, the line plane is reconstructed by using the center line of the line, and firstly, whether a measuring point is positioned in a straight line section or a curve section is determined, namely, the characteristic point of the line plane is identified.
And (3) removing interference points in the measuring line by combining MATLAB programming through a gradient threshold establishing method, identifying a straight line segment in the measuring line, and dividing the line into a combination of a straight line segment, a curve segment and a straight line segment through straight line segment coordinates, referring to FIG. 3, wherein FIG. 3 is a line measurement schematic diagram.
(1) Calculating the mileage of each measuring point
And taking the measurement coordinate system O-XY as a global coordinate system (hereinafter referred to as O-XY coordinate system), and calculating the line mileage value corresponding to each measuring point based on the coordinates of each measuring point. Because a seamless line is laid, the mileage value of each measuring point is fixed, the mileage value of the A point is set as the starting point of the line, and the mileage value of the A point is set as LaThen the mileage L of the subsequent measuring pointiCalculated according to the following formula (1):
Figure BDA0002075444250000041
wherein (x)i，yi) Is the coordinate of the ith measuring point, (x)i-1，yi-1) The coordinates of the (i-1) th measuring point.
S2 fitting the straight line segments to determine the slope of the straight line, and thus the declination angle of each curve segment.
And performing function fitting on the line of the straight line section by adopting a least square method, calculating the quadrant angles of the straight lines at the two ends of the curve section, determining the respective azimuth angles by the quadrant angles, further obtaining the azimuth angle difference between the straight lines at the two ends, and finally determining the deflection angle of the curve section by the azimuth angle difference. The method comprises the following specific steps:
1) calculating the quadrant angle
Fig. 4 is a schematic diagram of various quadrant angles, and as can be seen from fig. 4, the quadrant angles are calculated as shown in the following formula (2):
Figure BDA0002075444250000042
wherein the coordinate of the point A is (x)a，ya) Representing the starting point on a straight line in the reconstructed line shape, the coordinate of point B is (x)b，yb) Representing the second point on the straight line in the reconstructed line shape, immediately after point a. A. The positions of points B are shown in fig. 3 to 10.
2) Calculating azimuth
Fig. 5 is a schematic diagram of each azimuth angle, and the correlation between the quadrant angle and the azimuth angle can be seen in conjunction with fig. 4 and 5.
Exists when both points are located in the first quadrant (x)b＞xa,yb＞ya) AN azimuth angle AN ═ theta;
exists when both points are located in the second quadrant (x)b＜xa,yb＞ya) AN azimuth angle AN ═ pi-theta;
present when both points are in the third quadrant (x)b＜xa,yb＜ya) AN azimuth angle AN ═ π + θ;
exists when both points are located in the fourth quadrant (x)b＞xa,yb＜ya) And has AN azimuth angle AN of 2 pi-theta.
3) Calculating the azimuth angle difference of tangent lines at two sides of the curve
FIG. 6 is a schematic diagram of the calculation of the azimuth angle difference between the tangent lines on both sides of the curve, as shown in FIG. 6, the calculation of the azimuth angle difference is shown as follows:
β＝ANCD-ANAB (3)
beta represents the azimuth angle difference of tangent lines at two sides of the curve; AN (AN)CDIndicating C, D the azimuth of the line on which the point lies; AN (AN)ABIndicating the azimuth angle of the line on which point A, B lies.
4) Calculating the deflection angle
And calculating a deflection angle alpha according to the azimuth angle difference beta.
When beta is more than 0 and less than pi, alpha is beta, which is a right-bias curve; when pi < beta < 2 pi, alpha is 2 pi-beta, which is a left bias curve; when-pi < beta < 0, alpha is-beta, which is a left-hand offset curve; when-pi < beta < 2 pi, α -2 pi + β, which is a right-hand curve.
S3, based on the deflection angle of each curve section, the length of the easement curve and the radius of the circular curve are used as variables to establish a reconstruction curve, the dial value at the measuring point is used as a constraint function, the sum of squares of the dial values is minimum, and optimization is carried out to obtain a reconstructed plane line shape.
And writing a coordinate and dialing amount calculation formula of a reconstruction curve in the EXCEL, and obtaining a reconstructed plane line shape based on a planning solver in the EXCEL.
1. According to the industry specifications (TB 10098 and 2017 railway line design specifications),arbitrarily providing a group of circular curve radius R values meeting the specification requirement and gentle curve length l0And calculating the coordinate value in the reconstruction line corresponding to each measuring point based on the mileage of each measuring point.
(2) Calculating intersection point coordinates of reconstructed lines
From the above calculated azimuth angles of the straight lines at both ends of the curve segment, and coordinates of A, B, C and D are known, it is possible to calculate coordinates of the intersection of the straight lines at both ends of the curve segment, and calculation formulas of the coordinates of the intersection are shown in the following formulas (4) and (5).
Figure BDA0002075444250000051
Figure BDA0002075444250000052
Wherein the coordinate of the point A is (x)a，ya) Representing the starting point on one side straight line in the reconstructed line shape; the coordinate of the point B is (x)b，yb) Representing a second point on a straight line on one side in the reconstructed line shape, immediately after the point a; the coordinate of the point C is (x)c，yc) Indicating that the point before the end point on the straight line on the other side in the reconstructed line shape is positioned before the D point; the coordinate of the point C is (x)d，yd) And represents an end point on the other side straight line in the reconstructed line shape. A. The location of the four points B, C, D is shown in figures 3-10.
(3) According to the radius R of the initial circular curve and the gentle curve length l0Calculating elements and constants of the reconstruction curve, wherein the schematic diagram of each element of the reconstruction curve is shown in FIG. 7:
1) gentle curve angle beta0And (3) calculating:
Figure BDA0002075444250000061
2) calculation of the shift p in the relaxation curve:
Figure BDA0002075444250000062
3) calculation of sag m of the relief curve:
Figure BDA0002075444250000063
4) calculating tangent length T of the curve:
Figure BDA0002075444250000064
5) calculation of curve length L:
Figure BDA0002075444250000065
6) calculation of the tangent difference q: q is 2T-L;
wherein R is the radius of a circular curve, l0In order to reduce the curve length, the coordinates of the measurement points on the reconstructed line curve can be determined from the calculated elements.
(4) Mileage reckoning of principal points on reconstructed curves
And (4) calculating the mileage of the principal point of the easement curve based on the relationship between each element of the reconstructed curve and the length of the curve, wherein the mileage calculation formula of each principal point is as follows.
1) The mileage calculation formula of the intersection point (JD) of the straight lines at the two ends of the curve section is as follows:
Figure BDA0002075444250000066
2) the calculation result of the mileage at the forward and backward (ZH) point is as follows:
Figure BDA0002075444250000067
3) the calculation result of the mileage of the gentle circle (HY) point is as follows: l isHY＝LZH+l0；
4) The mileage estimation result of the curve middle (QZ) point is as follows:
Figure BDA0002075444250000068
5) the calculation result of the mileage at the round slow (YH) point is as follows: l isYH＝LHY+R×(α-2×β0)；
6) SlowThe straight (HZ) point mileage calculation result is as follows: l isHZ＝LYH+l0。
(5) Calculating the coordinates of each measuring point in the reconstruction curve
1) The line starting point A to the direct buffering (ZH) point corresponds to the coordinate (x) of the reconstructed curvei，yi) As shown in the following equations (6) and (7):
xi＝xJD-(LJD-Li)×cosANAB (6)
yi＝yJD-(LJD-Li)×sinANAB (7)
wherein x isiReconstructing an x coordinate in a measurement coordinate system O-XY for the measuring point i; y isiReconstructing a y coordinate in a measurement coordinate system O-XY for the measuring point i; x is the number ofJDThe x coordinate of the intersection point of the reconstructed line in a measurement coordinate system O-XY; y isJDThe y coordinate of the intersection point of the reconstructed line in a measurement coordinate system O-XY; l isiMileage of a measuring point i; l isJDThe intersection mileage is obtained; AN (AN)ABIs the azimuth angle of the line A, B in the measurement coordinate system O-XY.
When calculating the coordinates of the measurement points on the mitigation curve and the circular curve, firstly, the coordinates of each measurement point on the mitigation curve in a ZH-xy coordinate system are calculated, the ZH-xy coordinate system is shown in FIG. 8, the coordinate system takes the mitigation curve ZH as the origin, the ZH tangent as the x axis and the direction of the pointing intersection as the positive direction, a ZH-xy rectangular coordinate system is established, and the coordinate derivation from the vertical point to the measurement point of the section of the relief dot (ZH-HY) is performed under the coordinate system.
2) When the measuring point mileage is in a range from a direct buffering point (ZH) to a buffering circle (HY), the measuring point corresponds to the coordinate (x ') of the reconstruction curve'i，y′i) As shown in the following equations (8) and (9):
Figure BDA0002075444250000071
Figure BDA0002075444250000072
x′ithe coordinate of a measuring point i in a ZH-xy coordinate system is shown as the x coordinate; y'iIs the y coordinate of the m point in the ZH-xy coordinate system; l isiMileage of a measuring point i; l iszhThe mileage is a straight-slow point mileage; r is the radius of a circular curve; l0To moderate curve length; y 'when the curve is right-biased in the direction of mileage increase'iIs positive, y 'when the curve is left biased'iIs negative, namely is a left bias curve, y 'as shown in FIG. 8'iIs negative.
3) When the mileage of the measuring point i is in the interval from HY to YH, the measuring point corresponds to the coordinate (x 'on the reconstruction curve'i，y′i) The calculation is shown in equations (10) and (11):
Figure BDA0002075444250000073
Figure BDA0002075444250000074
x′ithe coordinate of a measuring point i in a ZH-xy coordinate system is shown as the x coordinate; y'iThe y coordinate of the measuring point i in a ZH-xy coordinate system; l isiMileage of a measuring point i; l isHYThe mileage of the slow dots is obtained; beta is a0To moderate curve angles; r is the radius of a circular curve; m is the gentle curve tangent distance; p is the transition distance in the relaxation curve.
According to the increasing direction of mileage, when the curve is deviated to the right, the curve is positive, and when the curve is deviated to the left, y'iIs negative, namely, is shown as a left bias curve y 'in FIG. 8'iIs negative.
4) When the mileage of the measuring point is in the interval from YH to HZ point, an HZ-x ' y ' coordinate system is established, in which the tangent line of the HZ point is taken as the x ' axis and the direction from the intersection point to the HZ point is taken as the positive direction, and the coordinate system is as shown in FIG. 9.
Under the coordinate system, the measuring point of the mileage between YH and HZ points corresponds to the coordinate (x ″) of the reconstructed curvei，y″i) The calculation formulas are shown in the following formulas (12) and (13).
Figure BDA0002075444250000075
Figure BDA0002075444250000076
x″iThe x coordinate of the measuring point i in the HZ-x 'y' coordinate system; y ″)iThe y coordinate of the measuring point i in the HZ-x 'y' coordinate system is shown; l isiMileage of point i, LHZThe slow straight point mileage is obtained; r is the radius of a circular curve; l0To moderate the curve length.
According to the increasing direction of the mileage of the line, when the curve is deviated to the right, y ″)iThe coordinate is positive; when the curve is left biased, y ″)iThe coordinates are negative.
After YH-HZ interval measuring point coordinates are calculated, the measuring point coordinates in HZ-x 'y' coordinates need to be converted into a ZH-xy coordinate system, FIG. 10 is a schematic diagram of converting the HZ-x 'y' coordinate system into a ZH-xy coordinate system, FIG. 11 is a schematic diagram of the position relationship between the measuring coordinate system and the ZH-xy coordinate system and the HZ-x 'y' coordinate system, and referring to FIGS. 10 and 11, the corresponding coordinate conversion calculation formula is shown as the following formula (14). The measuring point coordinate conversion calculation formula is as follows:
Figure BDA0002075444250000081
wherein, gamma is the azimuth angle of the x axis of the HZ-x 'y' coordinate system in the ZH-xy coordinate system, and when the curve is deviated to the right, gamma is alpha; when the curve is left-biased, gamma is-alpha, and alpha is a bias angle. (x'HZ，y′HZ) The calculation formula is shown in the following equations (15) and (16) for the coordinates of the HZ point in the ZH-xy coordinate system.
x′HZ＝T(1+cosα) (15)
y′HZ＝±Tsinα (16)
Wherein T is the tangent length of the curve; alpha is a declination angle.
Y 'when the curve is right-biased'HZTaking a positive value; curve left offset, y'HZTaking a negative value.
The coordinates of the curve segment (including the circle curve and the easement curve) calculated in the ZH-xy coordinate system are transferred to the measurement coordinate system, and the coordinate conversion formula is shown as the following formula (17).
Figure BDA0002075444250000082
Wherein, ANABIs the azimuth angle of the x-axis of the ZH-XY coordinate system in the measurement coordinate system O-XY.
(xZH，yZH) The calculation formula is shown in the following equations (18) and (19) for the coordinates of the ZH point in the measurement coordinate system O-XY.
xZH＝xJD-(LJD-LZH)×cosANAB (18)
yZH＝yJD+(LJD-LZH)×sinANAB (19)
Wherein x isZHThe x coordinate of a straight slow point of the reconstructed curve in a measurement coordinate system O-XY; y isZHIs the y coordinate of the straight slow point of the reconstructed curve in the measurement coordinate system O-XY; x is the number ofJDThe x coordinate of a straight slow point of the reconstructed curve in a measurement coordinate system O-XY; y isJDIs the y coordinate of the straight slow point of the reconstructed curve in the measurement coordinate system O-XY; l isJDThe intersection point mileage of the reconstructed curve is obtained; l isZHThe mileage is a straight slow point mileage of a reconstructed curve; AN (AN)ABIs the azimuth angle of the line A, B in the measurement coordinate system O-XY.
5) When the mileage of the measuring point is on the rear straight line, the measuring point corresponds to the coordinate (x) of the reconstructed curvei，yi) As shown in the following formulas (20) and (21).
xi＝xJD+(Li-LJD+q)×cosANCD (20)
yi＝yJD+(Li-LJD+q)×sinANCD (21)
Wherein x isiReconstructing an x coordinate in a measurement coordinate system O-XY for the measuring point i; y isiReconstructing a y coordinate in a measurement coordinate system O-XY for the measuring point i; x is the number ofJDFor reconfiguring linesThe x coordinate of the intersection point in a measurement coordinate system O-XY; y isJDThe y coordinate of the intersection point of the reconstructed line in a measurement coordinate system O-XY; l isiMileage of a measuring point i; q is the difference of tangent flexure; l isJDThe intersection mileage is obtained; AN (AN)CDIs the azimuth angle of the line A, B.
2 calculating the dialing amount of each measuring point
The dialing amount of each measuring point is the distance from the coordinate of the existing measuring point at the same mileage to the coordinate of the measuring point corresponding to the reconstruction curve, and the calculation formula is shown as the following formula (22).
Figure BDA0002075444250000083
Wherein (X)i，Yi) Is the x, y coordinate of the existing measuring point, (x)iYi) is the coordinate of the measured point corresponding to the reconstructed curve, ΔiThe dial amount of the measuring point i is measured.
It should be noted that: if the line includes a plurality of curves and straight lines, the length of the line between the two easement curves needs to be used as a constraint variable. The line reconstruction process comprises the following steps:
(1) the method is characterized in that an MATLAB program is combined to remove interference points in a measuring line through a gradient threshold establishing method, straight line segments in the measuring line are identified, the line is segmented through straight line segment coordinates, n intersection points are inevitable if n curves are totally provided, n +1 straight lines are necessary, all the lines are numbered from 1 to n in sequence, and a schematic diagram is shown in FIG. 12.
(2) And fitting each straight line segment by adopting a least square method, solving the mileage of each measuring point on the line by using the formula (1), repeating the reconstruction process of S2-S3 on each section of curve line, and sequentially solving the mileage of a slow point, a slow round point, a curved middle point, a circle slow point and a slow straight point of each section of line.
The calculation formula of the length of the included straight line is as shown in formula (23) or formula (24)
Ljz＝Li+1(zh)-Li(hz) (23)
Ljz-clip linear length; l isi+1(zh)-mileage of the (i + 1) th curve at the straight slow point; l isi(hz)Ith curveThe gentle straight point mileage.
Figure BDA0002075444250000091
Ljz-clip linear length; x is the number ofi+1(JD)-x coordinate of the intersection of the (i + 1) th curve; y isi+1(JD)-y-coordinate of the intersection of the (i + 1) th curve; x is the number ofi(JD)-x-coordinate of the intersection of the ith curve; y isi(JD)-y-coordinate of the intersection of the ith curve; t isi+1-tangent length of the (i + 1) th curve; t isi-tangent length of ith curve;
3. and writing a coordinate and dialing amount calculation formula of a reconstruction curve in the EXCEL, and obtaining a reconstructed plane line shape based on a planning solver in the EXCEL.
Reading segmented coordinates into EXCEL, deducing based on a formula made in 2, compiling a related parameter calculation formula, optimizing the line shape through a self-contained planning solver in the EXCEL, and providing a reasonable plane reconstruction line shape, wherein the step comprises the following steps:
and S31, segmenting the lines, and sequentially writing the coordinates of each segment of line into the corresponding position of the EXCEL. The line reconstruction design table is divided into two parts, referring to fig. 13 and 14, fig. 13 is a basic parameter calculation schematic diagram of the line reconstruction design table, fig. 14 is a coordinate method integer curve schematic diagram of the line reconstruction design table, and 13-a is a parameter calculation table of a reconstruction line; 13-b is an azimuth angle calculation interface diagram of the reconstructed line; 13-c is a calculation interface diagram of the intersection point of the reconstructed line; 13-d is a reconstructed line curve comprehensive element calculation interface diagram; 13-e is a reconstructed line curve mileage and coordinate calculation interface diagram.
S32, setting the initial curve length l0The radius R of the circular curve, and compiling a calculation formula for reconstructing a line coordinate and a dialing amount in the EXCEL, wherein a line reconstruction coordinate interface diagram is shown in figure 15, a dialing amount calculation interface diagram is shown in figure 16, and figure 15-a is a calculation interface diagram for reconstructing a line x coordinate; fig. 15-b reconstructs the calculation of the line y-coordinate.
S33, carrying out flattening based on self-contained planning solver in EXCELAnd (5) reconstructing the facial line shape. Setting the sum of squares of the dialing distances as an optimization target to minimize the sum of squares; based on the correlation between the dial amount (i.e. dial distance) of the measuring point and the radius, deflection angle and the length of the easement curve, the easement curve length value l0 and the radius R of the circular curve are used as independent variables, and the length l of the easement curve is continuously changed0And the circle radius R respectively calculates the dialing value of each measuring point and the length mileage of the included straight line between the two curves. The curve length l is eased based on the existing railway line design rule and railway technical management rule0The circle radius R, the clamp line length and the specified measurement point dialing allowance are used as constraint functions, and a target function is optimized based on a self-contained planning solver in the EXCEL, so that a reasonable plane reconstruction line shape is obtained, wherein a schematic diagram of the optimization process of the plane reconstruction line shape is shown in FIG. 17, and FIG. 17-a is a set optimization target interface diagram; FIG. 17-b is a set variable interface diagram; FIG. 17-c is a diagram of a set circular curve radius constraint interface; FIG. 17-d is a diagram of a set circular curve radius constraint interface; FIG. 17-e is an interface diagram of a constraint condition for setting a dial quantity of a measurement point; FIG. 17-f is a set solution options interface diagram.
Example two
The embodiment is an embodiment of simulation by adopting the line plane linear reconstruction design method on the railway bridge, and in order to verify the reasonability of the reconstruction method provided by the invention, a typical working point is selected for line plane reconstruction design. The total length of the line is 1.94km, and according to the constraint requirement of a line plane given by TB10098-2017 (railway line design specification), the line meets the following constraint requirement:
1. minimum length of circular curve or straight line: 80 m;
2. minimum circular curve radius: 400 m;
3. minimum relief curve length: 40m, rounding to 1m precision;
4. the specified measurement dial amount is less than the dial allowance (this requirement is not present in embodiment two).
Table 1 below is the actual measured point coordinates measured at the total station; table 2 shows the dial amount of each measurement point after linear reconstruction by the method, wherein the negative sign is the upper pick and the positive sign is the outer dial; table 3 is the reconstruction curve main parameters; table 4 is the coordinates of the reconstructed line shape; fig. 18 is a curvature comparison graph after line reconstruction.
TABLE 1 actual measurement Point coordinates
Figure BDA0002075444250000101
Figure BDA0002075444250000111
TABLE 2 Dial quantity of each measurement point
Point number Dialing amount (mm) Point number Dialing amount (mm) Point number Dialing amount (mm)
1 -44.17 33 -28.70 65 -53.02
2 -5.36 34 5.14 66 -45.24
3 14.94 35 9.77 67 -3.18
4 -31.48 36 7.31 68 18.44
5 1.40 37 -17.14 69 7.72
6 4.33 38 -4.72 70 -29.42
7 -69.23 39 31.68 71 -19.07
8 -12.72 40 -12.25 72 -20.38
9 -55.12 41 -51.06 73 -79.84
10 -1.70 42 3.05 74 8.40
11 4.62 43 1.17 75 -26.79
12 1.73 44 -0.69 76 -0.57
13 43.94 45 -35.82 77 -43.76
14 -20.46 46 21.03 78 -10.12
15 -37.64 47 -10.75 79 3.78
16 -1.66 48 6.63 80 32.88
17 2.21 49 12.01 81 -2.08
18 38.61 50 23.54 82 -44.85
19 -13.94 51 -0.60 83 -5.79
20 -0.32 52 33.72 84 -39.28
21 -30.04 53 -1.00 85 -58.54
22 8.47 54 44.52 86 5.59
23 68.11 55 -14.60 87 17.38
24 -0.50 56 15.90 88 45.65
25 12.92 57 5.24 89 -24.01
26 -12.92 58 28.36 90 -22.01
27 -3.65 59 8.28 91 -6.90
28 -12.49 60 0.76 92 0.51
29 -30.02 61 4.68 93 2.07
30 10.59 62 0.00 94 -1.05
31 -77.81 63 -25.01 95 -36.66
32 21.93 64 41.21 96 33.68
Table 3 main parameters of the reconstructed curves
Figure BDA0002075444250000112
Figure BDA0002075444250000121
TABLE 4 reconstructed curve coordinates
Figure BDA0002075444250000122
The standard railway line consists of five parts, namely a front straight line, a front easement curve, a circular curve, a rear easement curve and a rear straight line. The curvature of any point on the straight line segment is zero, the curvature of any point on the circular curve is 1/R, and the curvature of any point on the gentle curve segment is gradually increased to the curvature value of the circular curve from the curvature value of the starting point of the gentle curve. From the above analysis, it can be seen that, for a certain standard curve in the railway line, the curvature diagram is a trapezoid, and as can be seen from fig. 18, the reconstructed line includes two curves, and the curvature of the reconstructed curve is substantially a trapezoid, which satisfies the characteristics of the conventional curve line. As can be seen from table 3, the radius of the circular curve of the first curve is 602.107m, the length of the circular curve is 249.855m, the length of the single relaxing curve is 109m, the radius of the circular curve of the second curve is 1492.364m, the length of the circular curve is 259.385m, the length of the single relaxing curve is 79m, the length of the straight line between the two curves is 405.391m by using the formula (24), the reconstructed curve meets the requirements of the specification, and the reconstructed line can be applied to the actual line on the railway bridge.
EXAMPLE III
The embodiment is an embodiment of performing simulation by using the line shape reconstruction design method for the line on the railway bridge, and a typical work point 2 is selected for line plane reconstruction design. The total length of the line is 2.52km, the whole line is laid on the bridge, the line comprises a curve, the first three constraint conditions of the line are the same as those of the reconstruction embodiment II, the curve part of the line is influenced by the building limit, the pulling quantity of a measuring point on the curve is required to be less than 50mm, and the line is reconstructed as follows.
Wherein, table 5 is the original coordinates of the measuring points measured by the total station, table 6 is the reconstructed line drawing amount, the thickened part is the drawing amount of the measuring points of the curve part, table 7 is the reconstructed line curve element, table 8 is the reconstructed curve coordinates, and fig. 19 is the line curvature diagram before and after the line reconstruction.
TABLE 5 measurement Point original coordinates
Figure BDA0002075444250000131
Figure BDA0002075444250000141
TABLE 6 measurement of dialing amount
Figure BDA0002075444250000142
Figure BDA0002075444250000151
Table 7 main parameters of the reconstructed curves
Figure BDA0002075444250000152
TABLE 8 reconstructed Curve coordinates
Figure BDA0002075444250000153
Figure BDA0002075444250000161
As can be seen from fig. 19, the reconstructed line includes a curve, and the curvature of the reconstructed curve is substantially trapezoidal, which satisfies the conventional curve line characteristics. As can be seen from table 7, the radius of the circular curve of the reconstructed curve is 2040.675m, the length of the circular curve is 248.764m, the length of the single gentle curve is 55m, the maximum pulling amount of the measuring point on the curve is 43.90mm (the black number in table 6 is the pulling amount of the measuring point of the curve section), which is less than 50mm of the specification requirement, the reconstructed curve meets the specification requirement, and the reconstructed line can be applied to the actual line on the railway bridge.
From the above description of the embodiments, it is clear to those skilled in the art that the present invention can be implemented by software plus necessary general hardware platform. Based on such understanding, the technical solutions of the present invention may be embodied in the form of a software product, which may be stored in a storage medium, such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method according to the embodiments or some parts of the embodiments.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (3)

1. A planar line shape reconstruction design method for a line on a railway bridge is characterized by comprising the following steps:
measuring the coordinates of the center line of a track on a railway bridge by using a total station, and dividing straight line and curve sections in a measuring line;
fitting the straight line sections to determine the slope of the straight line, and further determining the deflection angle of each curve section;
based on the deflection angle of each curve section, establishing a reconstruction curve by taking the length of a relaxation curve and the radius of a circular curve as variables, and optimizing by taking the dial value at a measuring point as a constraint function and taking the sum of squares of the dial values as a target to obtain a reconstructed planar line shape, wherein the method comprises the following steps of: compiling a coordinate and dialing amount calculation formula of a reconstruction curve in EXCEL, and obtaining a reconstructed plane line shape based on a planning solver in the EXCEL;
further comprising: if the line comprises multiple straight lines and multiple curves, the length L of the straight line between two adjacent curves is usedjzAs a constraint function;
the method for obtaining the coordinates of the reconstructed curve is as follows:
(1) calculating the mileage of each measuring point
Taking a measurement coordinate system O-XY as a global coordinate system and based on each measuring pointCalculating the line mileage value corresponding to each measuring point by the coordinates; because a seamless line is laid, the mileage value of each measuring point is fixed, the mileage value of the A point is set as the starting point of the line, and the mileage value of the A point is set as LaThen the mileage L of the subsequent measuring pointiCalculated according to the following formula (1):
Figure FDA0003166439580000011
wherein (x)i，yi) Is the coordinate of the ith measuring point, (x)i-1，yi-1) Coordinates of the (i-1) th measuring point are obtained;
s2, fitting the straight line sections to determine the slope of the straight line and further determine the deflection angle of each curve section;
performing function fitting on the line of the straight line section by adopting a least square method, calculating the quadrant angles of the straight lines at the two ends of the curve section, determining the respective azimuth angles by the quadrant angles, further obtaining the azimuth angle difference between the straight lines at the two ends, and finally determining the deflection angle of the curve section by the azimuth angle difference; the method comprises the following specific steps:
1) calculating the quadrant angle
The quadrant angle is calculated as shown in the following equation (2):
Figure FDA0003166439580000012
wherein the coordinate of the point A is (x)a，ya) Representing the starting point on a straight line in the reconstructed line shape, the coordinate of point B is (x)b，yb) Representing a second point on the straight line in the reconstructed line shape, immediately after point a;
2) calculating azimuth
Exists when both points are located in the first quadrant (x)b＞xa,yb＞ya) AN azimuth angle AN ═ theta;
exists when both points are located in the second quadrant (x)b＜xa,yb＞ya) AN azimuth angle AN ═ pi-theta;
present when both points are in the third quadrant (x)b＜xa,yb＜ya) AN azimuth angle AN ═ π + θ;
exists when both points are located in the fourth quadrant (x)b＞xa,yb＜ya) AN azimuth angle AN 2 pi-theta;
3) calculating the azimuth angle difference of tangent lines at two sides of the curve
The azimuthal difference is calculated as follows:
β＝ANCD-ANAB (3)
beta represents the azimuth angle difference of tangent lines at two sides of the curve; AN (AN)CDIndicating C, D the azimuth of the line on which the point lies; AN (AN)ABIndicating A, B the azimuth angle of the line on which the point lies;
4) calculating the deflection angle
Calculating a deflection angle alpha according to the azimuth angle difference beta;
when beta is more than 0 and less than pi, alpha is beta, which is a right-bias curve; when pi < beta < 2 pi, alpha is 2 pi-beta, which is a left bias curve; when-pi < beta < 0, alpha is-beta, which is a left-hand offset curve; when-pi < beta < 2 pi, alpha is 2 pi + beta, which is a right-bias curve;
s3, based on the deflection angle of each curve section, establishing a reconstruction curve by taking the length of the easement curve and the radius of the circular curve as variables, and optimizing by taking the dial value at the measuring point as a constraint function and taking the minimum sum of squares of the dial values as a target to obtain a reconstructed plane line shape;
compiling a coordinate and dialing amount calculation formula of a reconstruction curve in EXCEL, and obtaining a reconstructed plane line shape based on a planning solver in the EXCEL;
(2) calculating intersection point coordinates of reconstructed lines
From the above calculated azimuth angles of the straight lines at the two ends of the curve segment, and coordinates of A, B, C and D are known, the coordinates of the intersection point of the straight lines at the two ends of the curve segment can be calculated, and the calculation formula of the intersection point coordinates is shown in the following formulas (4) and (5);
Figure FDA0003166439580000021
Figure FDA0003166439580000022
wherein the coordinate of the point A is (x)a，ya) Representing the starting point on one side straight line in the reconstructed line shape; the coordinate of the point B is (x)b，yb) Representing a second point on a straight line on one side in the reconstructed line shape, immediately after the point a; the coordinate of the point C is (x)c，yc) Indicating that the point before the end point on the straight line on the other side in the reconstructed line shape is positioned before the D point; the coordinate of the point D is (x)d，yd) Indicating an end point on the other side straight line in the reconstructed line shape;
(3) according to the radius R of the initial circular curve and the gentle curve length l0Calculating a reconstruction curve element and a constant, wherein:
1) gentle curve angle beta0And (3) calculating:
Figure FDA0003166439580000023
2) calculation of the shift p in the relaxation curve:
Figure FDA0003166439580000024
3) calculation of sag m of the relief curve:
Figure FDA0003166439580000025
4) calculating tangent length T of the curve:
Figure FDA0003166439580000026
5) calculation of curve length L:
Figure FDA0003166439580000027
6) calculation of the tangent difference q: q is 2T-L;
wherein R is the radius of a circular curve，l0In order to moderate the curve length, the coordinates of each measuring point on the reconstructed line curve can be determined according to each element calculated above;
(4) mileage reckoning of principal points on reconstructed curves
Calculating the mileage of the principal point of the easement curve based on the relationship between each element of the reconstructed curve and the length of the curve, wherein the calculation formula of the mileage of each principal point is as follows;
1) the mileage calculation formula of the intersection point (JD) of the straight lines at the two ends of the curve section is as follows:
Figure FDA0003166439580000031
2) the calculation result of the mileage at the forward and backward (ZH) point is as follows:
Figure FDA0003166439580000032
3) the calculation result of the mileage of the gentle circle (HY) point is as follows: l isHY＝LZH+l0；
4) The mileage estimation result of the curve middle (QZ) point is as follows:
Figure FDA0003166439580000033
5) the calculation result of the mileage at the round slow (YH) point is as follows: l isYH＝LHY+R×(α-2×β0)；
6) The calculation result of the mileage of the moderate straight (HZ) point is as follows: l isHZ＝LYH+l0；
(5) Calculating the coordinates of each measuring point in the reconstruction curve
1) The line starting point A to the direct buffering (ZH) point corresponds to the coordinate (x) of the reconstructed curvei，yi) As shown in the following equations (6) and (7):
xi＝xJD-(LJD-Li)×cos ANAB (6)
yi＝yJD-(LJD-Li)×sin ANAB (7)
wherein x isiReconstructing an x coordinate in a measurement coordinate system for the measuring point i; y isiReconstructing a y coordinate of the measuring point i in a measuring coordinate system; x is the number ofJDX coordinates of the intersection point of the reconstruction line in a measurement coordinate system; y isJDThe y coordinate of the intersection point of the reconstructed line in the measurement coordinate system is obtained; l isiMileage of a measuring point i; l isJDThe intersection mileage is obtained; AN (AN)ABIs the azimuth angle of the line A, B in the measurement coordinate system O-XY;
when calculating the coordinates of the measuring points on the easement curve and the circular curve, firstly calculating the coordinates of each measuring point on the easement curve in a ZH-xy coordinate system, wherein the coordinate system takes the prior easement curve ZH as an origin, takes a ZH tangent as an x axis and takes the direction of the pointing intersection point as a positive direction, establishing a ZH-xy rectangular coordinate system, and deducing the coordinates from a vertical slow point to a slow dot (ZH-HY) section measuring point under the coordinate system;
2) when the measuring point mileage is in a range from a direct buffering point (ZH) to a buffering circle (HY), the measuring point corresponds to the coordinate (x ') of the reconstruction curve'i，y′i) As shown in the following equations (8) and (9):
Figure FDA0003166439580000034
Figure FDA0003166439580000035
x′ithe coordinate of a measuring point i in a ZH-xy coordinate system is shown as the x coordinate; y'iIs the y coordinate of the m point in the ZH-xy coordinate system; l isiMileage of a measuring point i; l iszhThe mileage is a straight-slow point mileage; r is the radius of a circular curve; l0To moderate curve length; y 'when the curve is right-biased in the direction of mileage increase'iIs positive, y 'when the curve is left biased'iIs negative;
3) when the mileage of the measuring point i is in the interval from HY to YH, the measuring point corresponds to the coordinate (x 'on the reconstruction curve'i，y′i) The calculation is shown in equations (10) and (11):
Figure FDA0003166439580000041
Figure FDA0003166439580000042
x′ithe coordinate of a measuring point i in a ZH-xy coordinate system is shown as the x coordinate; y'iThe y coordinate of the measuring point i in a ZH-xy coordinate system; l isiMileage of a measuring point i; l isHYThe mileage of the slow dots is obtained; beta is a0To moderate curve angles; r is the radius of a circular curve; m is the gentle curve tangent distance; p is the transition distance of the transition curve;
according to the increasing direction of mileage, when the curve is deviated to the right, the curve is positive, and when the curve is deviated to the left, y'iIs negative;
4) when the measuring point mileage is in the interval from YH to HZ, establishing an HZ-x ' y ' coordinate system which takes the tangent line of the HZ point as an x ' axis and the direction from the intersection point to the HZ point as the positive direction;
under the coordinate system, the measuring point of the mileage between YH and HZ points corresponds to the coordinate (x ″) of the reconstructed curvei，y″i) The calculation formulas are shown in the following formulas (12) and (13);
Figure FDA0003166439580000043
Figure FDA0003166439580000044
x″ithe x coordinate of the measuring point i in the HZ-x 'y' coordinate system; y ″)iThe y coordinate of the measuring point i in the HZ-x 'y' coordinate system is shown; l isiMileage of point i, LHZThe slow straight point mileage is obtained; r is the radius of a circular curve; l0To moderate curve length;
according to the increasing direction of the mileage of the line, when the curve is deviated to the right, y ″)iThe coordinate is positive; when the curve is left biased, y ″)iThe coordinates are negative;
after YH-HZ interval measuring point coordinates are calculated, converting the measuring point coordinates in HZ-x 'y' coordinates into a ZH-xy coordinate system, wherein the corresponding coordinate conversion calculation formula is shown as the following formula (14); the measuring point coordinate conversion calculation formula is as follows:
Figure FDA0003166439580000045
wherein, gamma is the azimuth angle of the x axis of the HZ-x 'y' coordinate system in the ZH-xy coordinate system, and when the curve is deviated to the right, gamma is alpha; when the curve is deviated left, gamma is equal to-alpha, and alpha is a deviation angle; (x'HZ，y′HZ) The calculation formula is shown in the following formulas (15) and (16) for the coordinates of the HZ point in the ZH-xy coordinate system;
x′HZ＝T(1+cosα) (15)
y′HZ＝±Tsinα (16)
wherein T is the tangent length of the curve; alpha is a declination angle;
y 'when the curve is right-biased'HZTaking a positive value; curve left offset, y'HZTaking a negative value;
transferring the coordinates of the curve section calculated in the ZH-xy coordinate system into a measurement coordinate system, wherein a coordinate conversion formula is shown as the following formula (17);
Figure FDA0003166439580000051
wherein, ANABIs the azimuth angle of the x axis of the ZH-XY coordinate system in the measurement coordinate system O-XY;
(xZH，yZH) The calculated formula is shown in the following formulas (18) and (19) for the coordinates of the ZH point in the measurement coordinate system O-XY;
xZH＝xJD-(LJD-LZH)×cos ANAB (18)
yZH＝yJD+(LJD-LZH)×sin ANAB (19)
wherein x isZHThe x coordinate of a straight slow point of the reconstructed curve in a measurement coordinate system O-XY; y isZHIs the y coordinate of the straight slow point of the reconstructed curve in the measurement coordinate system O-XY; x is the number ofJDThe x coordinate of a straight slow point of the reconstructed curve in a measurement coordinate system O-XY; y isJDIs the y coordinate of the straight slow point of the reconstructed curve in the measurement coordinate system O-XY; l isJDThe intersection point mileage of the reconstructed curve is obtained; l isZHThe mileage is a straight slow point mileage of a reconstructed curve; AN (AN)ABIs the azimuth angle of the line A, B in the measurement coordinate system O-XY;
5) when the mileage of the measuring point is on the rear straight line, the measuring point corresponds to the coordinate (x) of the reconstructed curvei，yi) As shown in the following formulae (20) and (21);
xi＝xJD+(Li-LJD+q)×cos ANCD (20)
yi＝yJD+(Li-LJD+q)×sin ANCD (21)
wherein x isiReconstructing an x coordinate in a measurement coordinate system for the measuring point i; y isiReconstructing a y coordinate of the measuring point i in a measuring coordinate system; x is the number ofJDX coordinates of the intersection point of the reconstruction line in a measurement coordinate system; y isJDThe y coordinate of the intersection point of the reconstructed line in the measurement coordinate system is obtained; l isiMileage of a measuring point i; q is the difference of tangent flexure; l isJDThe intersection mileage is obtained; AN (AN)CDIs the azimuth angle of the line A, B.
2. The method of claim 1, wherein said measuring line track centerline coordinates on a railroad bridge with a total station, dividing straight and curved line segments in a survey line, comprises: and (3) removing interference electricity in the measuring line by combining MATLAB programming through a method of establishing a gradient threshold, identifying straight line segments in the measuring line, segmenting the line through straight line segment coordinates, and calculating the mileage of each measuring point.
3. The method of claim 1, wherein said fitting said straight line segments to determine the slope of the straight line and thus the declination angle of each curve segment comprises: and performing function fitting on the line of the straight line section by adopting a least square method, calculating the quadrant angles of the straight lines at the two ends of the curve section, determining the respective azimuth angles by the quadrant angles so as to obtain the azimuth angle difference between the straight lines at the two ends, and determining the deflection angle of the curve section by the azimuth angle difference.
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