CN113373827A - Ballastless track smoothness control method for bridge pier settlement section - Google Patents

Ballastless track smoothness control method for bridge pier settlement section Download PDF

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CN113373827A
CN113373827A CN202110916965.5A CN202110916965A CN113373827A CN 113373827 A CN113373827 A CN 113373827A CN 202110916965 A CN202110916965 A CN 202110916965A CN 113373827 A CN113373827 A CN 113373827A
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point
adjustment
adjusting
fastener
vertical curve
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CN113373827B (en
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时瑾
张雨潇
杨飞
李再帏
龙许友
王英杰
孙宪夫
高雅
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Beijing Jiaotong University
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    • E—FIXED CONSTRUCTIONS
    • E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
    • E01D—CONSTRUCTION OF BRIDGES, ELEVATED ROADWAYS OR VIADUCTS; ASSEMBLY OF BRIDGES
    • E01D21/00—Methods or apparatus specially adapted for erecting or assembling bridges
    • E—FIXED CONSTRUCTIONS
    • E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
    • E01B—PERMANENT WAY; PERMANENT-WAY TOOLS; MACHINES FOR MAKING RAILWAYS OF ALL KINDS
    • E01B35/00—Applications of measuring apparatus or devices for track-building purposes
    • E01B35/12—Applications of measuring apparatus or devices for track-building purposes for measuring movement of the track or of the components thereof under rolling loads, e.g. depression of sleepers, increase of gauge
    • E—FIXED CONSTRUCTIONS
    • E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
    • E01D—CONSTRUCTION OF BRIDGES, ELEVATED ROADWAYS OR VIADUCTS; ASSEMBLY OF BRIDGES
    • E01D19/00—Structural or constructional details of bridges
    • E01D19/12—Grating or flooring for bridges; Fastening railway sleepers or tracks to bridges
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
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Abstract

The invention discloses a ballastless track smoothness control method for a bridge pier settlement section, which is based on track smoothness management requirements and bridge design information, optimizes and designs the longitudinal section line shape of a track, constructs a fastener adjustment optimization model, controls periodic uneven height by a deviation poor constraint method, controls the uneven long wave in the track by a midpoint vector method and a vector difference method, solves and obtains the fastener adjustment which accords with an adjustable range according to an optimization theory, guides ballastless track fine tuning operation and evaluates the operation effect, further improves the optimization design parameters and the constraint control conditions of the model according to the evaluation result, and calculates and obtains a final fastener adjustment optimization scheme. The method can fully make up the defect that the traditional fine adjustment method has poor effect of correcting the irregularity of the track of the settlement section of the pier, and can effectively improve the smoothness state and the fine adjustment operation efficiency of the ballastless track of the settlement section of the pier.

Description

Ballastless track smoothness control method for bridge pier settlement section
Technical Field
The invention relates to the technical field of railway engineering and optimization processing, in particular to a ballastless track smoothness control method for a bridge pier settlement section.
Background
The high-speed railway in China largely adopts a bridge structure, after the high-speed railway is built and operated, a plurality of bridge foundations can generate settlement deformation under the comprehensive action of various factors, ballastless tracks laid on a bridge floor are longitudinally connected, the resistance to pier settlement is poor, and bending deformation can also follow the settlement deformation, so that periodic track irregularity taking the bridge span length as a unit is easily caused, interference is generated on wheel-track contact, the safety and the stability of a train are deteriorated, and in order to ensure the running performance of a high-speed train, the ballastless tracks need to be finely adjusted, and the geometric smoothness state of the tracks is recovered.
The' guide for fine adjustment operation of ballastless track engineering construction of high-speed railway (iron construction [2009]674 ]) requires that the elevation deviation of a track surface is +4/-6mm, the allowable deviation of a track center line and a design center line is 10mm, however, the actual position of the track is greatly deviated from the design position under the influence of bridge pier settlement, the adjustment range of a fastener is limited, if the adjustment is completely carried out according to the specified allowable deviation, the dilemma that the required adjustment amount is inconsistent with the actual adjustment amount is caused, and therefore how to obtain the position of the design line which is suitable for the integral settlement deformation becomes the key for solving the problem. The static height irregularity management requirements of the track are indicated in the specifications of a ballastless track engineering construction fine adjustment operation guide of a high-speed railway, a high-speed railway engineering measurement specification and the like, the ballastless track located in a bridge structure is influenced by bridge pier settlement, the height irregularity shows a periodic change rule, the management capacity of a detection string on irregularity is weakened, a more effective adjustment scheme needs to be further explored, the adjustment quantity of a fastener is optimized and calculated, the adaptability of fine adjustment operation on bridge pier settlement is improved, and the smoothness state of the track is improved.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a ballastless track smoothness control method for a bridge pier settlement section, and the technical problems to be solved by the invention are as follows: the method for optimizing the adjustment quantity of the ballastless track is designed to compensate for the optimal linear shape of the track of the integral settlement of the bridge foundation, combines a static smoothness management standard, researches an optimization method for the adjustment quantity of the ballastless track adapting to the unsmooth periodic deformation, and provides reference for controlling the smoothness of the line of the settlement section of the bridge pier and improving the fine adjustment operation effect of the ballastless track.
In order to achieve the above purposes, the technical scheme adopted by the invention is as follows:
the method for controlling the smoothness of the ballastless track of the bridge pier settlement section effectively corrects the irregularity of the track of the bridge pier settlement section as a target to calculate the adjustment amount of the fastener, and specifically comprises the following steps:
A. the ballastless track adjusting point is the position of a fastener on one side of the reference track, three-dimensional coordinate data of the ballastless track reference track collected by the track detector is collected and used as measuring data of the adjusting point, the measuring data of the adjusting point is fitted again by using an orthogonal least square method, a new longitudinal section design linear shape is constructed, longitudinal section design parameters according with the actual line state after the bridge pier is settled are obtained, and the longitudinal section deviation between the actually measured linear shape and the design linear shape is calculated.
B. According to the fastener adjustable range, the bridge span design length, the track smoothness management value and the poor management value, a fastener adjustment quantity optimization model for regulating the periodic unevenness of the bridge pier settlement section is established, the fastener adjustment quantity of the whole section of the line to be regulated is calculated, the periodic unevenness is eliminated, and a fastener adjustment quantity optimization scheme is formulated.
C. And (4) implementing fine adjustment operation according to the fastener adjustment optimization scheme, judging whether the track irregularity caused by pier settlement is effectively controlled, and further optimizing the fastener adjustment to obtain a final fastener adjustment optimization scheme.
On the basis of the above scheme, step a specifically includes:
a-1, calculating the gradient change rate of the adjusting point, performing linear segmentation according to the gradient change rate, preliminarily identifying the position of the variable gradient point, and judging the type of the adjusting point, wherein the type of the adjusting point comprises the following steps: the device comprises a slope section adjusting point and a vertical curve adjusting point, wherein the adjusting point in the slope section range is called the slope section adjusting point, and the adjusting point in the vertical curve range is called the vertical curve adjusting point; fitting the front and rear slope sections by adopting an orthogonal least square method to obtain a function equation of the front and rear slope sections, and calculating the mileage and elevation of a variable slope point and the gradient of the front and rear slope sections by using the function equation of the front and rear slope sections; fitting a vertical curve by adopting an orthogonal least square method to obtain a circle center coordinate
Figure 171313DEST_PATH_IMAGE001
And radius
Figure 212606DEST_PATH_IMAGE002
And calculating vertical curve design information, wherein the vertical curve design information comprises: mileage, elevation, etc. of straight dots and circles.
A-2, judging the type of the adjusting point according to the vertical curve design information obtained by calculation in the step A-1, fitting the front slope section and the rear slope section and the vertical curve again, calculating the mileage difference between the front line element boundary point and the rear line element boundary point, setting a threshold value according to the actual state of the line, repeating the step A-1 when the mileage difference is larger than the threshold value until the mileage difference is smaller than the threshold value, wherein the line element boundary points tend to be stable at the moment, ending iteration, and obtaining the design parameters of the vertical section according with the actual line state after the integral settlement of the pier.
A-3, calculating the deviation of the slope section adjusting point and the deviation of the vertical curve adjusting point based on the design parameters of the vertical section, wherein the specific formula of the deviation of the slope section adjusting point is as follows:
Figure 222150DEST_PATH_IMAGE003
(1)
in the formula (I), the compound is shown in the specification,
Figure 100002_DEST_PATH_IMAGE004
adjusting point knitting for slope sectionNumber;
Figure 521413DEST_PATH_IMAGE005
adjusting the point deviation for the slope section, wherein the unit is mm;
Figure 918896DEST_PATH_IMAGE006
the mileage of a slope section adjusting point is in units of m;
Figure 444556DEST_PATH_IMAGE007
measuring elevation for a slope section adjusting point in a unit of m;
Figure 257791DEST_PATH_IMAGE008
designing slope of a slope section linear equation for the position of the slope section adjusting point;
Figure 552506DEST_PATH_IMAGE009
designing a slope section linear equation constant term for the position of the slope section adjusting point;
Figure 652049DEST_PATH_IMAGE010
to determine the coefficients when
Figure 602687DEST_PATH_IMAGE011
When the temperature of the water is higher than the set temperature,
Figure 281930DEST_PATH_IMAGE012
(ii) a When in use
Figure 717239DEST_PATH_IMAGE013
When the temperature of the water is higher than the set temperature,
Figure 518842DEST_PATH_IMAGE014
。
deviation of the vertical curve adjustment point
Figure 753514DEST_PATH_IMAGE015
The specific formula of (a) is as follows:
Figure 642973DEST_PATH_IMAGE016
(2)
in the formula (I), the compound is shown in the specification,
Figure 974597DEST_PATH_IMAGE017
numbering the adjusting points of the vertical curve;
Figure 291309DEST_PATH_IMAGE015
adjusting the point deviation for the vertical curve, wherein the unit is mm;
Figure 278856DEST_PATH_IMAGE018
is the radius of the vertical curve, in m;
Figure 299902DEST_PATH_IMAGE019
mileage of a point is adjusted for a vertical curve in units of m;
Figure 220453DEST_PATH_IMAGE020
measuring the elevation for the vertical curve adjustment point in m;
Figure 239225DEST_PATH_IMAGE021
the mileage of the center of the vertical curve is in m;
Figure 448489DEST_PATH_IMAGE022
is the elevation of the circle center of the vertical curve, and the unit is m;
Figure 72893DEST_PATH_IMAGE023
to determine the coefficients, when the vertical curve is a concave curve,
Figure 723318DEST_PATH_IMAGE024
when the vertical curve is a convex curve,
Figure 975307DEST_PATH_IMAGE025
。
on the basis of the above scheme, the fastener adjustment optimization model in step B includes:
objective function
Figure 468606DEST_PATH_IMAGE026
And a constraint; said aboutThe bundle condition includes: poor deviation constraint of periodic irregularity, fastener adjustment constraint of adjustment points, and detection chord length of
Figure 503558DEST_PATH_IMAGE027
Has a midpoint vector distance constraint and a detected chord length of
Figure 100002_DEST_PATH_IMAGE028
The vector distance difference constraint of (1);
the track smoothness management values include: a ride control value for the mid-point vector distance and a ride control value for the vector distance difference.
On the basis of the scheme, the step B specifically comprises the following steps:
b-1, summing the fastener adjustment quantity of the slope section adjustment point in the line to be adjusted and the absolute value of the fastener adjustment quantity of the vertical curve adjustment point to realize the minimum sum value as a target function
Figure 601964DEST_PATH_IMAGE026
Design objective, objective function
Figure 87172DEST_PATH_IMAGE026
Comprises the following steps:
Figure 943132DEST_PATH_IMAGE029
(3)
in the formula (I), the compound is shown in the specification,
Figure 375251DEST_PATH_IMAGE030
the adjustment amount of the fastener for the slope section adjustment point is in mm;
Figure 265846DEST_PATH_IMAGE031
the adjustment amount of the fastener which is the adjustment point of the vertical curve is in mm;
Figure DEST_PATH_IMAGE032
the number of the points is adjusted for the slope section,
Figure 125218DEST_PATH_IMAGE033
；
Figure 327529DEST_PATH_IMAGE034
the number of points is adjusted for the vertical curve,
Figure 969863DEST_PATH_IMAGE035
。
b-2. influenced by bridge pier settlement, the deviation of the vertical section is in periodic change, and the objective function which needs to be established in the step B-1
Figure 571090DEST_PATH_IMAGE036
On the basis, an adjusting point control equation is established by adopting a deviation poor constraint method to control periodic irregularity and slope section adjusting point deviation
Figure 7887DEST_PATH_IMAGE037
Adjustment amount of fastener with slope section adjustment point
Figure 697495DEST_PATH_IMAGE038
The remaining deviation of the adjusted slope section obtained by algebraic operation is
Figure 612361DEST_PATH_IMAGE039
Deviation of adjustment point of vertical curve
Figure 336604DEST_PATH_IMAGE040
Adjustment of fastener to vertical curve adjustment point
Figure 944302DEST_PATH_IMAGE041
The remaining deviation of the adjusted vertical curve obtained by algebraic operation is
Figure 121206DEST_PATH_IMAGE042
The formula is as follows:
Figure 839763DEST_PATH_IMAGE043
（4）。
determining the design length of the bridge span according to the design information of the bridge
Figure 621774DEST_PATH_IMAGE044
To do so by
Figure 525008DEST_PATH_IMAGE045
Determining poor management values based on line conditions and acceptance requirements for chord length control
Figure 330153DEST_PATH_IMAGE046
The poor constraint formula for controlling the deviation of the periodic irregularity is as follows:
Figure 977035DEST_PATH_IMAGE047
（5）
in the formula (I), the compound is shown in the specification,
Figure 285657DEST_PATH_IMAGE048
is a poor management value in mm;
Figure 359792DEST_PATH_IMAGE049
the residual deviation of the slope section adjusting point at the position of half bridge span design length away from the adjusting point is measured in mm,
Figure 121075DEST_PATH_IMAGE050
the residual deviation of the vertical curve adjusting point at the position of half bridge span design length away from the adjusting point is measured in mm.
Wherein, the
Figure 574577DEST_PATH_IMAGE051
And
Figure 737705DEST_PATH_IMAGE052
the formula of (a) is as follows:
Figure 982742DEST_PATH_IMAGE053
（6）
in the formula (I), the compound is shown in the specification,
Figure 496900DEST_PATH_IMAGE054
is composed of
Figure 485584DEST_PATH_IMAGE055
The number of the contained adjusting points;
Figure 503219DEST_PATH_IMAGE056
adjusting the fastener adjustment amount of the slope section adjustment point at the half bridge span design length position away from the adjustment point;
Figure 387998DEST_PATH_IMAGE057
and adjusting the fastener adjusting amount of the vertical curve adjusting point at the position of half bridge span design length from the adjusting point.
B-3, setting the fastener adjusting amount of the slope section adjusting point according to the actual fastener adjusting amount range
Figure 248507DEST_PATH_IMAGE058
Fastener adjustment for constraint and vertical curve adjustment points
Figure 650670DEST_PATH_IMAGE059
The constraint is specifically as follows:
Figure 913024DEST_PATH_IMAGE060
（7）
the formula (7) can be converted into formula (8):
Figure 640808DEST_PATH_IMAGE061
（8）
in the formula (I), the compound is shown in the specification,
Figure 723034DEST_PATH_IMAGE062
the lower limit of the fastener adjusting amount is in mm;
Figure 194466DEST_PATH_IMAGE063
the upper limit of the fastener adjustment amount is in mm.
B-4, the midpoint vector distance and the vector distance difference of the track are effective indexes reflecting the smoothness state and need to be calculated according to the management value of the actual construction operationWhich exerts an effective control in which the mid-point vector detects a chord length of
Figure 576906DEST_PATH_IMAGE064
Vector distance difference detection chord length of
Figure 210013DEST_PATH_IMAGE065
；
Based on adjusting the residual deviation of the rear slope section
Figure 245446DEST_PATH_IMAGE066
And the residual deviation of the adjusted vertical curve
Figure 100002_DEST_PATH_IMAGE067
Calculating the vector distance and the vector distance difference of the midpoint, comparing the calculation result with the corresponding smoothness management value, and correcting the fastener adjustment amount of the slope section adjustment point in time
Figure 848466DEST_PATH_IMAGE068
Adjustment of fastener to vertical curve adjustment point
Figure 819833DEST_PATH_IMAGE069
To meet regulatory value constraint requirements.
Wherein the detection chord length is
Figure 686158DEST_PATH_IMAGE064
The midpoint vector distance constraint equation of (1) is as follows:
Figure 946238DEST_PATH_IMAGE070
（9）
in the formula (I), the compound is shown in the specification,
Figure 759473DEST_PATH_IMAGE071
for measuring chord length
Figure 116505DEST_PATH_IMAGE064
The starting point of (a) is left with deviation and the starting point is positioned on a slope section,
Figure 91414DEST_PATH_IMAGE072
For measuring chord length
Figure 901107DEST_PATH_IMAGE073
The starting point of (a) has a residual deviation and is located on a vertical curve,
Figure 252454DEST_PATH_IMAGE074
For measuring chord length
Figure 198414DEST_PATH_IMAGE073
The end point of the end point is remained with deviation and the end point is positioned on the slope section,
Figure 344224DEST_PATH_IMAGE075
For measuring chord length
Figure 375634DEST_PATH_IMAGE076
The end point of (2) has residual deviation and is positioned on the vertical curve;
Figure 100002_DEST_PATH_IMAGE077
is the smoothness management value of the mid-point vector distance.
Detecting a chord length of
Figure 330339DEST_PATH_IMAGE065
The vector distance difference constraint formula is as follows:
Figure 130805DEST_PATH_IMAGE078
（10）
in the formula (I), the compound is shown in the specification,
Figure 100002_DEST_PATH_IMAGE079
for measuring chord length
Figure 306571DEST_PATH_IMAGE080
The starting point of (a) is left with deviation and the starting point is positioned on a slope section,
Figure 100002_DEST_PATH_IMAGE081
For measuring chord length
Figure 294119DEST_PATH_IMAGE080
The starting point of (a) has a residual deviation and is located on a vertical curve,
Figure 987268DEST_PATH_IMAGE082
For measuring chord length
Figure 907820DEST_PATH_IMAGE080
The end point of the end point is remained with deviation and the end point is positioned on the slope section,
Figure 100002_DEST_PATH_IMAGE083
For measuring chord length
Figure 926592DEST_PATH_IMAGE080
The end point of (2) has residual deviation and is positioned on the vertical curve;
Figure 100002_DEST_PATH_IMAGE084
for measuring chord length
Figure 135856DEST_PATH_IMAGE080
The check point of (a) is left offset and the check point is located in the slope segment,
Figure DEST_PATH_IMAGE085
for measuring chord length
Figure 226172DEST_PATH_IMAGE080
The accounting point is always at the rear side of the adjusting point and is away from the adjusting point by a chord length
Figure DEST_PATH_IMAGE086
；
Figure DEST_PATH_IMAGE087
The vector distance difference is used as a smoothness management value;
Figure DEST_PATH_IMAGE088
calculating coefficients for the vector distance differences;
the calculation formula of the vector distance difference calculation coefficient is as follows:
Figure DEST_PATH_IMAGE089
（11）
Figure DEST_PATH_IMAGE090
the number of the accounting points is numbered,
Figure DEST_PATH_IMAGE091
the string end point numbers are detected for the vector distance differences,
Figure DEST_PATH_IMAGE092
the chord start point numbers are detected for the vector distance differences,
Figure DEST_PATH_IMAGE093
the adjustment points are numbered, when the type of the adjustment point is a slope adjustment point,
Figure DEST_PATH_IMAGE094
when the type of the adjusting point is the adjusting point of the vertical curve,
Figure DEST_PATH_IMAGE095
。
b-5, integrating the formulas (5), (8), (9) and (10) in the steps B-1 to B-4 to form a comprehensive optimization constraint condition, and converting the comprehensive optimization constraint condition into a matrix inequality, wherein the specific formula is as follows:
Figure DEST_PATH_IMAGE096
（12）
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE097
is a chord length
Figure DEST_PATH_IMAGE098
The number of the included slope section adjusting points is,
Figure DEST_PATH_IMAGE099
is a chord length
Figure 637781DEST_PATH_IMAGE098
The number of the included vertical curve adjusting points is,
Figure DEST_PATH_IMAGE100
is a chord length
Figure 420929DEST_PATH_IMAGE080
The number of included slope section adjusting points;
Figure DEST_PATH_IMAGE101
is a chord length
Figure 385998DEST_PATH_IMAGE080
The number of the included vertical curve adjusting points;
Figure DEST_PATH_IMAGE102
adjustment of fastener for slope adjustment point
Figure DEST_PATH_IMAGE103
Adjustment of fastener to vertical curve adjustment point
Figure DEST_PATH_IMAGE104
Corresponding coefficient matrix with number of rows
Figure DEST_PATH_IMAGE105
The number of columns of the coefficient matrix is
Figure DEST_PATH_IMAGE106
；
Figure DEST_PATH_IMAGE107
Adjustment of fastener for slope adjustment point
Figure DEST_PATH_IMAGE108
Adjustment of fastener to vertical curve adjustment point
Figure DEST_PATH_IMAGE109
Corresponding constraint matrix, constraintNumber of rows of matrix
Figure DEST_PATH_IMAGE110
The number of columns is 1;
Figure DEST_PATH_IMAGE111
a fastener adjustment matrix for the slope and vertical curve adjustment points, the number of rows of the fastener adjustment matrix being
Figure DEST_PATH_IMAGE112
The number of columns is 1.
Solving the matrix inequality according to an optimization theory, calculating to obtain the fastener adjustment quantity of the whole section of the line slope section adjustment point and the whole section of the line vertical curve adjustment point, wherein the calculation result meets the constraint of the fastener adjustment quantity, has the adjustment capacity on the periodic irregularity of the track caused by the settlement of the pier, and accords with the management regulation of maintenance specifications on the static smoothness of the ballastless track, thereby formulating a fastener adjustment quantity optimization scheme.
On the basis of the scheme, the step C specifically comprises the following steps:
c-1, guiding constructors to accurately adjust the reference rail by adopting a fastener adjustment quantity optimization scheme in a ballastless track of a bridge pier settlement section, measuring internal geometric parameters of the track after the reference rail is adjusted to a correct position, and adjusting a non-reference rail according to the internal geometric parameters, wherein the internal geometric parameters of the track comprise: gauge, gauge rate of change, level and twist, etc.
And C-2, after the first operation is finished, acquiring track irregularity information after fine adjustment by using a track inspection instrument, evaluating the implementation effect of the fastener adjustment quantity optimization scheme in the first operation process, adjusting the design parameters of the longitudinal section in the step A according to the adaptability of the scheme to the integral deviation of the pier settlement section, adjusting the constraint control conditions in the step B according to the improvement capacity of the scheme to the periodic track irregularity, recalculating the fastener adjustment quantity of the remaining line to be adjusted, and obtaining the final fastener adjustment quantity optimization scheme.
The invention has the beneficial effects that:
through carrying out optimal design and comprehensive constraint condition to the ballastless track, the optimal adjustment quantity of the fastener is obtained by calculation, the integral deviation of the line caused by the settlement of the pier is facilitated to be fully adapted, the periodic irregularity of the track caused by the settlement of the pier is facilitated to be rectified, and the smoothness state and the fine adjustment operation efficiency of the ballastless track at the settlement section of the pier are further improved. Firstly, the influence of bridge pier settlement on an upper structure is fully considered about the treatment of track irregularity, the design parameters which accord with the actual state of a line are obtained by utilizing the fitting of an orthogonal least square method, and the contradiction between the large integral offset of the track and the limited adjustable range of a fastener is relieved; secondly, adding a poor deviation constraint method to carry out smoothness control aiming at periodic unevenness of the track caused by bridge pier settlement, integrating midpoint vector constraint, vector difference constraint and fastener adjustable quantity constraint into the smoothness control, calculating fastener adjustment quantities of a slope section adjustment point and a vertical curve adjustment point by combining an optimization theory, and guiding constructors to finish fine adjustment of the unevenness of the track; finally, the method further improves the effect of the fastener adjustment optimization scheme on the treatment of the irregularity of the rail at the settlement section of the pier by evaluating the implementation effect of the fastener adjustment optimization scheme in the operation process, adjusting the optimization design parameters and the constraint control conditions.
The method provides a scientific method for making the adjustment quantity optimization scheme of the ballastless track fastener at the settlement section of the pier, and research results have important scientific value and guiding significance for fine adjustment operation of the ballastless track.
Drawings
The invention has the following drawings:
FIG. 1 is a schematic diagram illustrating an optimization effect of track irregularity of a settlement section of a pier;
fig. 2 is a flow chart of the ballastless track smoothness control method of the invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings 1 to 2.
A ballastless track smoothness control method for a bridge pier settlement section comprises the following specific implementation modes:
1) and the ballastless track adjusting point is the position of a fastener on one side of the reference track, three-dimensional coordinate data of the ballastless track collected by the track detector is collected and used as measurement data of the adjusting point, the vertical section is re-fitted by using an orthogonal least square method, actual design parameters conforming to the overall deviation of the line after the pier is settled are obtained, and the deviation of the vertical section is calculated.
(a) Calculating the gradient change rate of the adjusting point, performing linear segmentation according to the change rate information, preliminarily identifying the position of the variable slope point, and judging the type of the adjusting point, wherein the adjusting point in the range of the slope segment is called a slope segment adjusting point, and the adjusting point in the range of the vertical curve is called a vertical curve adjusting point; and obtaining slope section equations before and after the variable slope point by adopting an orthogonal least square method, wherein the specific calculation formula of the slope equation is as follows:
Figure DEST_PATH_IMAGE113
（13）
Figure DEST_PATH_IMAGE114
（14）
Figure DEST_PATH_IMAGE115
（15）
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE116
；
Figure DEST_PATH_IMAGE117
；
Figure DEST_PATH_IMAGE118
；
Figure DEST_PATH_IMAGE119
numbering the slope section adjusting points;
Figure DEST_PATH_IMAGE120
the mileage of a slope section adjusting point is in units of m;
Figure DEST_PATH_IMAGE121
measuring elevation for a slope section adjusting point in a unit of m;
Figure DEST_PATH_IMAGE122
the number of the points is adjusted for the slope section,
Figure DEST_PATH_IMAGE123
；
two sets of solutions can be obtained by solving the equations (14) and (15), one set of solution which enables the total deviation measurement line to be minimum is taken as a final gradient equation parameter, and the variable slope point mileage, the elevation and the front and rear slope section gradient related to the final gradient equation parameter are calculated.
Fitting a vertical curve by adopting an orthogonal least square method to obtain a circle center coordinate
Figure DEST_PATH_IMAGE124
And radius
Figure DEST_PATH_IMAGE125
And calculating straight dots and straight dot mileage of circles, wherein the specific calculation formula of the circular curve parameters is as follows:
Figure DEST_PATH_IMAGE126
（16）
Figure DEST_PATH_IMAGE127
（17）
Figure DEST_PATH_IMAGE128
（18）
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE129
；
Figure DEST_PATH_IMAGE130
；
Figure DEST_PATH_IMAGE131
；
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE132
；
Figure DEST_PATH_IMAGE133
；
Figure DEST_PATH_IMAGE134
；
Figure DEST_PATH_IMAGE135
；
Figure DEST_PATH_IMAGE136
；
Figure DEST_PATH_IMAGE137
numbering the adjusting points of the vertical curve;
Figure DEST_PATH_IMAGE138
mileage of a point is adjusted for a vertical curve in units of m;
Figure DEST_PATH_IMAGE139
measuring the elevation for the vertical curve adjustment point in m;
Figure DEST_PATH_IMAGE140
the number of points is adjusted for the vertical curve,
Figure 877676DEST_PATH_IMAGE141
。
(b) judging the type of the adjusting point again according to the new longitudinal section parameters, fitting the front slope section and the rear slope section and the vertical curve again, calculating the mileage difference of the line element boundary points of the front slope section and the rear slope section, setting a threshold value according to the actual state of the line, repeatedly calculating new longitudinal section design parameters when the mileage difference is larger than the threshold value until the mileage difference is smaller than the threshold value, indicating that the line element boundary points tend to be stable, ending iteration, and obtaining the longitudinal section design parameters which accord with the actual line state of the pier after the integral settlement.
(c) Based on the design parameters of the vertical section, calculating the deviation of the slope section adjusting point and the deviation of the vertical curve adjusting point, wherein the specific formula of the deviation of the slope section adjusting point is as follows:
Figure 382607DEST_PATH_IMAGE003
(1)
in the formula (I), the compound is shown in the specification,
Figure 602236DEST_PATH_IMAGE004
numbering the slope section adjusting points;
Figure 192617DEST_PATH_IMAGE005
adjusting the point deviation for the slope section, wherein the unit is mm;
Figure 152964DEST_PATH_IMAGE006
the mileage of a slope section adjusting point is in units of m;
Figure 777981DEST_PATH_IMAGE007
measuring elevation for a slope section adjusting point in a unit of m;
Figure 168511DEST_PATH_IMAGE008
designing slope of a slope section linear equation for the position of the slope section adjusting point;
Figure 246188DEST_PATH_IMAGE009
designing a slope section linear equation constant term for the position of the slope section adjusting point;
Figure 747577DEST_PATH_IMAGE010
to determine the coefficients when
Figure 227100DEST_PATH_IMAGE011
When the temperature of the water is higher than the set temperature,
Figure 788531DEST_PATH_IMAGE012
(ii) a When in use
Figure 353504DEST_PATH_IMAGE013
When the temperature of the water is higher than the set temperature,
Figure 658584DEST_PATH_IMAGE014
；
deviation of the vertical curve adjustment point
Figure 258192DEST_PATH_IMAGE015
The specific formula of (a) is as follows:
Figure 990525DEST_PATH_IMAGE016
(2)
in the formula (I), the compound is shown in the specification,
Figure 777216DEST_PATH_IMAGE017
numbering the adjusting points of the vertical curve;
Figure 885986DEST_PATH_IMAGE015
adjusting the point deviation for the vertical curve, wherein the unit is mm;
Figure 340101DEST_PATH_IMAGE018
is the radius of the vertical curve, in m;
Figure 977756DEST_PATH_IMAGE019
mileage of a point is adjusted for a vertical curve in units of m;
Figure 251742DEST_PATH_IMAGE020
measuring the elevation for the vertical curve adjustment point in m;
Figure 167133DEST_PATH_IMAGE021
the mileage of the center of the vertical curve is in m;
Figure 475755DEST_PATH_IMAGE022
is the elevation of the circle center of the vertical curve, and the unit is m;
Figure 549890DEST_PATH_IMAGE023
to determine the coefficients, when the vertical curve is a concave curve,
Figure 576752DEST_PATH_IMAGE024
when the vertical curve is a convex curve,
Figure 496166DEST_PATH_IMAGE025
。
2) according to the fastener adjustable quantity range, the bridge span design length, the track smoothness management value and the poor management value, a fastener adjustable quantity optimization model for treating the periodic unevenness of the bridge pier settlement section is established, and an objective function and constraint conditions of the model are established as follows.
a) Summing the fastener adjustment amount of the slope section adjustment point in the line to be adjusted and the absolute value of the fastener adjustment amount of the vertical curve adjustment point to realize the minimum sum value as a target function
Figure 924874DEST_PATH_IMAGE026
Design objective, objective function
Figure 169910DEST_PATH_IMAGE026
Comprises the following steps:
Figure 418489DEST_PATH_IMAGE029
(3)
in the formula (I), the compound is shown in the specification,
Figure 407173DEST_PATH_IMAGE030
the adjustment amount of the fastener for the slope section adjustment point is in mm;
Figure 690387DEST_PATH_IMAGE031
the adjustment amount of the fastener which is the adjustment point of the vertical curve is in mm;
Figure 106325DEST_PATH_IMAGE032
the number of the points is adjusted for the slope section,
Figure 842200DEST_PATH_IMAGE033
；
Figure 634575DEST_PATH_IMAGE034
the number of points is adjusted for the vertical curve,
Figure 772296DEST_PATH_IMAGE035
。
b) the deviation of the vertical section is periodically changed under the influence of the settlement of the pier, and an objective function needs to be established in the step B-1
Figure 359135DEST_PATH_IMAGE036
On the basis, an adjusting point control equation is established by adopting a deviation poor constraint method to control periodic irregularity and slope section adjusting point deviation
Figure 582306DEST_PATH_IMAGE037
Adjustment amount of fastener with slope section adjustment point
Figure 175442DEST_PATH_IMAGE038
The remaining deviation of the adjusted slope section obtained by algebraic operation is
Figure 167669DEST_PATH_IMAGE039
Deviation of adjustment point of vertical curve
Figure 925410DEST_PATH_IMAGE040
Adjustment of fastener to vertical curve adjustment point
Figure 635877DEST_PATH_IMAGE041
The remaining deviation of the adjusted vertical curve obtained by algebraic operation is
Figure 770055DEST_PATH_IMAGE042
The formula is as follows:
Figure 616788DEST_PATH_IMAGE043
（4）。
determining that the design length of the bridge span is 32m according to the bridge design information, determining that 2mm is a poor control value according to the line state and the acceptance requirement by taking 16m as the control chord length, and controlling the poor deviation constraint formula of the periodic irregularity as follows:
Figure DEST_PATH_IMAGE142
（19）
in the formula (I), the compound is shown in the specification,
Figure 279851DEST_PATH_IMAGE049
the residual deviation of the slope section adjusting point at the position of half bridge span design length away from the adjusting point is measured in mm,
Figure 336668DEST_PATH_IMAGE050
the residual deviation of the vertical curve adjusting point at the position of half bridge span design length away from the adjusting point is measured in mm,mthe number of the adjustment points contained in the string of 16 m.
The above-mentioned
Figure 149904DEST_PATH_IMAGE051
And
Figure 975777DEST_PATH_IMAGE052
the formula of (a) is as follows:
Figure 216266DEST_PATH_IMAGE053
（6）
in the formula (I), the compound is shown in the specification,
Figure 760379DEST_PATH_IMAGE056
adjusting the fastener adjustment amount of the slope section adjustment point at the half bridge span design length position away from the adjustment point;
Figure 111726DEST_PATH_IMAGE057
and adjusting the fastener adjusting amount of the vertical curve adjusting point at the position of half bridge span design length from the adjusting point.
c) The lower limit of the adjustable quantity of the actual fastener is-4 mm, the upper limit is 15mm, the adjustable quantity of the fastener of the slope section adjusting point and the vertical curve adjusting point is restricted according to the range, and the specific restriction formula is as follows:
Figure DEST_PATH_IMAGE143
（20）
that is, the formula (20) can be converted into the formula (21):
Figure DEST_PATH_IMAGE144
（21）。
d) according to the standard management requirements, the 10m normal vector, the 30m/5m vector distance difference and the 300m/150m vector distance difference of the track need to be effectively controlled, wherein the smoothness management value of a chord of 10m is 2mm, the smoothness management value of a chord of 30m is 2mm, and the smoothness management value of a chord of 300m is 10 mm.
Based on adjusting the residual deviation of the rear slope section
Figure DEST_PATH_IMAGE145
And the residual deviation of the adjusted vertical curve
Figure 591774DEST_PATH_IMAGE146
Calculating the vector distance and the vector distance difference of the midpoint, comparing the calculation result with the corresponding smoothness management value, and correcting the fastener adjustment amount of the slope section adjustment point in time
Figure DEST_PATH_IMAGE147
Adjustment of fastener to vertical curve adjustment point
Figure 596639DEST_PATH_IMAGE148
To meet regulatory value constraint requirements.
The specific constraint formula for the 10m chord midpoint vector distance is as follows:
Figure DEST_PATH_IMAGE149
（22）
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE150
the residual deviation of the starting point of the chord of 10m and the starting point of the chord is positioned in a slope segment,
Figure DEST_PATH_IMAGE151
The residual deviation of the starting point of the chord of 10m is obtained, and the starting point is positioned on the vertical curve,
Figure DEST_PATH_IMAGE152
Is 10m chord end point residual deviation and the end point is positioned on a slope segment,
Figure DEST_PATH_IMAGE153
The deviation remained for the 10m chord end point and the end point was located on the vertical curve.
The specific constraint formula for the 30m chordal distance difference is as follows:
Figure DEST_PATH_IMAGE154
（23）
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE155
the residual deviation of the starting point of the chord of 30m and the starting point of the chord is positioned in a slope segment,
Figure DEST_PATH_IMAGE156
The residual deviation of the starting point of the chord of 30m is obtained, and the starting point is positioned on the vertical curve,
Figure DEST_PATH_IMAGE157
The residual deviation of the chord end point of 30m and the end point is positioned on the slope segment,
Figure DEST_PATH_IMAGE158
The deviation is the residual deviation of the end point of the string of 30m, and the end point is positioned on the vertical curve;
Figure DEST_PATH_IMAGE159
the residual deviation of the accounting point is calculated for 30m chord and the accounting point is positioned on the slope segment,
Figure DEST_PATH_IMAGE160
and the residual deviation of the 30m chord check point is calculated, the check point is positioned on the vertical curve, and the 30m chord check point is always positioned at the rear side of the adjusting point and is 5m away from the adjusting point.
The specific constraint formula for the 300m chordal vector distance difference is as follows:
Figure 467862DEST_PATH_IMAGE154
（24）
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE161
the residual deviation of the starting point of the chord of 300m and the starting point of the chord is positioned in a slope segment,
Figure DEST_PATH_IMAGE162
The residual deviation of the starting point of the chord of 300m is obtained, and the starting point is positioned on the vertical curve,
Figure DEST_PATH_IMAGE163
The residual deviation of the chord end point of 300m and the end point is positioned on the slope segment,
Figure DEST_PATH_IMAGE164
The deviation is the residual deviation of the end point of the 300m chord, and the end point is positioned on the vertical curve;
Figure DEST_PATH_IMAGE165
the residual deviation of the check point is calculated for 300m chord and the check point is positioned in the slope segment,
Figure DEST_PATH_IMAGE166
the residual deviation of the chord check point is 300m, the check point is positioned on the vertical curve, and the chord check point of 300m is always behind the adjusting point and is 150m away from the adjusting point.
e) Integrating the formulas (19), (21), (22), (23) and (24) to form a comprehensive optimization constraint condition, and converting the comprehensive optimization constraint condition into a matrix inequality, wherein the matrix inequality is as follows:
Figure DEST_PATH_IMAGE167
（25）
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE168
the number of adjusting points contained in the string of 10 m;
Figure DEST_PATH_IMAGE169
adjustment of fastener for slope adjustment point
Figure DEST_PATH_IMAGE170
Adjustment of fastener to vertical curve adjustment point
Figure DEST_PATH_IMAGE171
Corresponding coefficient matrix with number of rows
Figure 793539DEST_PATH_IMAGE172
The number of columns of the coefficient matrix is
Figure DEST_PATH_IMAGE173
；
Figure DEST_PATH_IMAGE174
Adjustment of fastener for slope adjustment point
Figure 659251DEST_PATH_IMAGE170
Adjustment of fastener to vertical curve adjustment point
Figure 241542DEST_PATH_IMAGE171
Corresponding constraint matrix with row number of
Figure DEST_PATH_IMAGE175
The number of columns is 1;
Figure DEST_PATH_IMAGE176
a fastener adjustment matrix for the slope and vertical curve adjustment points, the number of rows of the fastener adjustment matrix being
Figure DEST_PATH_IMAGE177
The number of columns is 1.
Solving the matrix inequality according to an optimization theory, calculating to obtain the fastener adjustment quantity of the point to be adjusted of the whole section of line, wherein the calculation result meets the upper limit and the lower limit of the fastener adjustment quantity, has the adjustment capability on the periodic irregularity of the track caused by the settlement of the pier, and accords with the management regulation of maintenance specifications on the static smoothness of the ballastless track, thereby establishing the optimization scheme of the fastener adjustment quantity.
3) At the ballastless track of pier settlement section, implement the fine-tuning operation according to fastener adjustment optimization scheme, instruct constructor to adjust the benchmark rail, after the benchmark rail adjusted to the correct position, measure the inside geometric parameters of track to use this as the basis adjustment non-benchmark rail, wherein the inside geometric parameters of rail include: gauge, gauge rate of change, level, twist, etc.;
after the first fine adjustment operation is completed, the track inspection tester and the dynamic inspection vehicle are used for collecting the dynamic and static track irregularity after the fine adjustment, and data are collected for judging whether the track irregularity caused by the settlement of the pier is effectively controlled.
4) Calculating the long wave irregularity in the track of 30-300 m according to the track state information before and after adjustment, evaluating the implementation effect of the fastener adjustment amount in the first operation process, adjusting the optimal design parameters of least square fitting of a longitudinal section according to the adaptive capacity of the fastener adjustment amount optimization scheme to the integral deviation of the pier settlement section, adjusting the constraint control conditions of the fastener adjustment amount calculation model according to the improvement capacity of the fastener adjustment amount optimization scheme to the periodic track irregularity, recalculating the fastener adjustment amount of the remaining line to be operated, and obtaining the final fastener adjustment amount optimization scheme.
The method for calculating the adjustment quantity of the fastener, which is suitable for integral deviation and periodic irregularity of the ballastless track, guides constructors to accurately adjust the line of the settlement section of the pier, solves the problem of poor effect of the traditional ballastless track fine adjustment operation on the treatment of the irregularity of the track under the settlement deformation of the pier, and has important theoretical significance and engineering practical value.
Those not described in detail in this specification are within the skill of the art.

Claims (5)

1. The ballastless track smoothness control method for the bridge pier settlement section is characterized by comprising the following steps of:
A. the ballastless track adjusting point is the position of a fastener on one side of the reference track, three-dimensional coordinate data of the ballastless track reference track collected by a track detector is collected and used as measurement data of the adjusting point, the measurement data of the adjusting point is fitted again by using an orthogonal least square method, a new vertical section design linear shape is constructed, vertical section design parameters conforming to the actual line state after the bridge pier is settled are obtained, and vertical section deviation between the actually measured linear shape and the design linear shape is calculated;
B. establishing a fastener adjustment quantity optimization model for correcting the periodic uneven height of the settlement section of the pier according to the fastener adjustment quantity range, the bridge span design length, the track smoothness management value and the worse management value, calculating the fastener adjustment quantity of the whole section of line to be adjusted, eliminating the periodic uneven height, and making a fastener adjustment quantity optimization scheme;
C. and (4) implementing fine adjustment operation according to the fastener adjustment optimization scheme, judging whether the track irregularity caused by pier settlement is effectively controlled, and further optimizing the fastener adjustment to obtain a final fastener adjustment optimization scheme.
2. The ballastless track smoothness control method for the pier settlement section of claim 1, wherein the step a specifically comprises:
a-1, calculating the gradient change rate of the adjusting point, performing linear segmentation according to the gradient change rate, preliminarily identifying the position of the variable gradient point, and judging the type of the adjusting point, wherein the type of the adjusting point comprises the following steps: the device comprises a slope section adjusting point and a vertical curve adjusting point, wherein the adjusting point in the slope section range is called the slope section adjusting point, and the adjusting point in the vertical curve range is called the vertical curve adjusting point; fitting the front and rear slope sections by adopting an orthogonal least square method to obtain a function equation of the front and rear slope sections, and calculating the mileage and elevation of a variable slope point and the gradient of the front and rear slope sections by using the function equation of the front and rear slope sections; fitting a vertical curve by adopting an orthogonal least square method to obtain a circle center coordinate
Figure 105175DEST_PATH_IMAGE001
And radius
Figure 491157DEST_PATH_IMAGE002
And calculating vertical curve design information, wherein the vertical curve design information comprises: mileage and elevation of straight dots and round straight dots;
a-2, judging the type of the adjusting point according to the vertical curve design information obtained by calculation in the step A-1, fitting the front slope section and the rear slope section and the vertical curve again, calculating the mileage difference between the front line element boundary point and the rear line element boundary point, setting a threshold value according to the actual state of the line, repeating the step A-1 when the mileage difference is greater than the threshold value until the mileage difference is less than the threshold value, wherein the line element boundary points tend to be stable at the moment, ending iteration, and obtaining the design parameters of the vertical section according with the actual line state after the integral settlement of the pier;
a-3, calculating the deviation of the slope section adjusting point and the deviation of the vertical curve adjusting point based on the design parameters of the vertical section, wherein the specific formula of the deviation of the slope section adjusting point is as follows:
Figure 864370DEST_PATH_IMAGE003
(1)
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE004
numbering the slope section adjusting points;
Figure 321896DEST_PATH_IMAGE005
adjusting the point deviation for the slope section, wherein the unit is mm;
Figure 605110DEST_PATH_IMAGE006
the mileage of a slope section adjusting point is in units of m;
Figure 21047DEST_PATH_IMAGE007
measuring elevation for a slope section adjusting point in a unit of m;
Figure 756922DEST_PATH_IMAGE008
designing slope of a slope section linear equation for the position of the slope section adjusting point;
Figure 549298DEST_PATH_IMAGE009
designing a slope section linear equation constant term for the position of the slope section adjusting point;
Figure 687018DEST_PATH_IMAGE010
to determine the coefficients when
Figure 273857DEST_PATH_IMAGE011
When the temperature of the water is higher than the set temperature,
Figure 497028DEST_PATH_IMAGE012
(ii) a When in use
Figure 827515DEST_PATH_IMAGE013
When the temperature of the water is higher than the set temperature,
Figure 819742DEST_PATH_IMAGE014
；
deviation of the vertical curve adjustment point
Figure 845991DEST_PATH_IMAGE015
The specific formula of (a) is as follows:
Figure 556459DEST_PATH_IMAGE016
(2)
in the formula (I), the compound is shown in the specification,
Figure 425057DEST_PATH_IMAGE017
numbering the adjusting points of the vertical curve;
Figure 537370DEST_PATH_IMAGE015
adjusting the point deviation for the vertical curve, wherein the unit is mm;
Figure 466012DEST_PATH_IMAGE018
is the radius of the vertical curve, in m;
Figure 663775DEST_PATH_IMAGE019
mileage of a point is adjusted for a vertical curve in units of m;
Figure 336065DEST_PATH_IMAGE020
measuring the elevation for the vertical curve adjustment point in m;
Figure 568463DEST_PATH_IMAGE021
the mileage of the center of the vertical curve is in m;
Figure 933585DEST_PATH_IMAGE022
is the elevation of the circle center of the vertical curve, and the unit is m;
Figure 353065DEST_PATH_IMAGE023
to determine the coefficients, when the vertical curve is a concave curve,
Figure 829046DEST_PATH_IMAGE024
when the vertical curve is a convex curve,
Figure 650371DEST_PATH_IMAGE025
。
3. the ballastless track ride comfort control method for the pier settlement section according to claim 2, wherein the fastener adjustment optimization model of step B comprises: objective function
Figure 186395DEST_PATH_IMAGE026
And a constraint; the constraint conditions include: poor deviation constraint of periodic irregularity, fastener adjustment constraint of adjustment points, and detection chord length of
Figure DEST_PATH_IMAGE027
Has a midpoint vector distance constraint and a detected chord length of
Figure DEST_PATH_IMAGE028
The vector distance difference constraint of (1);
the track smoothness management values include: a ride control value for the mid-point vector distance and a ride control value for the vector distance difference.
4. The ballastless track smoothness control method for the pier settlement section of claim 3, wherein the step B specifically comprises:
b-1, summing the fastener adjustment quantity of the slope section adjustment point in the line to be adjusted and the absolute value of the fastener adjustment quantity of the vertical curve adjustment point to realize the minimum sum value as a target function
Figure 889909DEST_PATH_IMAGE026
Design objective, objective function
Figure 190088DEST_PATH_IMAGE026
Comprises the following steps:
Figure DEST_PATH_IMAGE029
(3)
in the formula (I), the compound is shown in the specification,
Figure 459395DEST_PATH_IMAGE030
the adjustment amount of the fastener for the slope section adjustment point is in mm;
Figure DEST_PATH_IMAGE031
the adjustment amount of the fastener which is the adjustment point of the vertical curve is in mm;
Figure 635162DEST_PATH_IMAGE032
the number of the points is adjusted for the slope section,
Figure DEST_PATH_IMAGE033
；
Figure 622709DEST_PATH_IMAGE034
the number of points is adjusted for the vertical curve,
Figure DEST_PATH_IMAGE035
；
b-2. influenced by bridge pier settlement, the deviation of the vertical section is in periodic change, and the objective function which needs to be established in the step B-1
Figure 909334DEST_PATH_IMAGE036
On the basis, an adjusting point control equation is established by adopting a deviation poor constraint method to control periodic irregularity and slope section adjusting point deviation
Figure DEST_PATH_IMAGE037
Adjustment amount of fastener with slope section adjustment point
Figure 705252DEST_PATH_IMAGE038
The remaining deviation of the adjusted slope section obtained by algebraic operation is
Figure DEST_PATH_IMAGE039
Deviation of adjustment point of vertical curve
Figure 379816DEST_PATH_IMAGE040
Adjustment of fastener to vertical curve adjustment point
Figure DEST_PATH_IMAGE041
The remaining deviation of the adjusted vertical curve obtained by algebraic operation is
Figure 526763DEST_PATH_IMAGE042
The formula is as follows:
Figure DEST_PATH_IMAGE043
（4）
determining the design length of the bridge span according to the design information of the bridge
Figure DEST_PATH_IMAGE044
To do so by
Figure 213484DEST_PATH_IMAGE045
Determining poor management values based on line conditions and acceptance requirements for chord length control
Figure DEST_PATH_IMAGE046
The poor constraint formula for controlling the deviation of the periodic irregularity is as follows:
Figure DEST_PATH_IMAGE047
（5）
in the formula (I), the compound is shown in the specification,
Figure 926225DEST_PATH_IMAGE048
is a poor management value in mm;
Figure DEST_PATH_IMAGE049
the residual deviation of the slope section adjusting point at the position of half bridge span design length away from the adjusting point is measured in mm,
Figure DEST_PATH_IMAGE050
setting the residual deviation of the vertical curve adjusting point at the position of half bridge span design length from the adjusting point in mm;
the above-mentioned
Figure DEST_PATH_IMAGE051
And
Figure DEST_PATH_IMAGE052
the formula of (a) is as follows:
Figure DEST_PATH_IMAGE053
（6）
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE054
is composed of
Figure DEST_PATH_IMAGE055
The number of the contained adjusting points;
Figure DEST_PATH_IMAGE056
adjusting the fastener adjustment amount of the slope section adjustment point at the half bridge span design length position away from the adjustment point;
Figure DEST_PATH_IMAGE057
adjusting the fastener adjustment amount of the vertical curve adjustment point at the position of half bridge span design length from the adjustment point;
b-3, setting the fastener adjusting amount of the slope section adjusting point according to the actual fastener adjusting amount range
Figure DEST_PATH_IMAGE058
Fastener adjustment for constraint and vertical curve adjustment points
Figure DEST_PATH_IMAGE059
The constraint is specifically as follows:
Figure DEST_PATH_IMAGE060
（7）
the formula (7) can be converted into formula (8):
Figure DEST_PATH_IMAGE061
（8）
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE062
the lower limit of the fastener adjusting amount is in mm;
Figure DEST_PATH_IMAGE063
the upper limit of the fastener adjusting amount is in mm;
b-4, the midpoint vector distance and the vector distance difference of the track are effective indexes reflecting the smoothness state and need to be calculated according to the management value of the actual construction operationWhich exerts an effective control in which the mid-point vector detects a chord length of
Figure DEST_PATH_IMAGE064
Vector distance difference detection chord length of
Figure DEST_PATH_IMAGE065
；
Based on adjusting the residual deviation of the rear slope section
Figure DEST_PATH_IMAGE066
And the residual deviation of the adjusted vertical curve
Figure DEST_PATH_IMAGE067
Calculating the vector distance and the vector distance difference of the midpoint, comparing the calculation result with the corresponding smoothness management value, and correcting the fastener adjustment amount of the slope section adjustment point in time
Figure DEST_PATH_IMAGE068
Adjustment of fastener to vertical curve adjustment point
Figure DEST_PATH_IMAGE069
To meet regulatory value constraint requirements;
wherein the detection chord length is
Figure 532875DEST_PATH_IMAGE064
The midpoint vector distance constraint equation of (1) is as follows:
Figure DEST_PATH_IMAGE070
（9）
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE071
for measuring chord length
Figure 760594DEST_PATH_IMAGE064
Residual deviation of starting point and starting pointAt the slope section,
Figure DEST_PATH_IMAGE072
For measuring chord length
Figure DEST_PATH_IMAGE073
The starting point of (a) has a residual deviation and is located on a vertical curve,
Figure DEST_PATH_IMAGE074
For measuring chord length
Figure 451338DEST_PATH_IMAGE073
The end point of the end point is remained with deviation and the end point is positioned on the slope section,
Figure DEST_PATH_IMAGE075
For measuring chord length
Figure 818253DEST_PATH_IMAGE073
The end point of (2) has residual deviation and is positioned on the vertical curve;
Figure DEST_PATH_IMAGE076
is the smoothness management value of the midpoint vector distance;
detecting a chord length of
Figure DEST_PATH_IMAGE077
The vector distance difference constraint formula is as follows:
Figure DEST_PATH_IMAGE078
（10）
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE079
for measuring chord length
Figure 631357DEST_PATH_IMAGE077
The starting point of (a) is left with deviation and the starting point is positioned on a slope section,
Figure DEST_PATH_IMAGE080
For measuring chord length
Figure 80793DEST_PATH_IMAGE077
The starting point of (a) has a residual deviation and is located on a vertical curve,
Figure DEST_PATH_IMAGE081
For measuring chord length
Figure 512912DEST_PATH_IMAGE077
The end point of the end point is remained with deviation and the end point is positioned on the slope section,
Figure DEST_PATH_IMAGE082
For measuring chord length
Figure 465824DEST_PATH_IMAGE077
The end point of (2) has residual deviation and is positioned on the vertical curve;
Figure DEST_PATH_IMAGE083
for measuring chord length
Figure 325196DEST_PATH_IMAGE077
The check point of (a) is left offset and the check point is located in the slope segment,
Figure DEST_PATH_IMAGE084
for measuring chord length
Figure 668452DEST_PATH_IMAGE077
The accounting point is always at the rear side of the adjusting point and is away from the adjusting point by a chord length
Figure 635753DEST_PATH_IMAGE085
；
Figure 912013DEST_PATH_IMAGE086
The vector distance difference is used as a smoothness management value;
Figure 473445DEST_PATH_IMAGE087
calculating coefficients for the vector distance differences;
the calculation formula of the vector distance difference calculation coefficient is as follows:
Figure 38418DEST_PATH_IMAGE088
（11）
Figure 343498DEST_PATH_IMAGE089
the number of the accounting points is numbered,
Figure 677527DEST_PATH_IMAGE090
the string end point numbers are detected for the vector distance differences,
Figure 409860DEST_PATH_IMAGE091
the chord start point numbers are detected for the vector distance differences,
Figure 462129DEST_PATH_IMAGE092
the adjustment points are numbered, when the type of the adjustment point is a slope adjustment point,
Figure 305320DEST_PATH_IMAGE093
when the type of the adjusting point is the adjusting point of the vertical curve,
Figure 759435DEST_PATH_IMAGE094
；
b-5, integrating the formulas (5), (8), (9) and (10) in the steps B-1 to B-4 to form a comprehensive optimization constraint condition, and converting the comprehensive optimization constraint condition into a matrix inequality, wherein the specific formula is as follows:
Figure 397090DEST_PATH_IMAGE095
（12）
in the formula (I), the compound is shown in the specification,
Figure 202235DEST_PATH_IMAGE096
is a chord length
Figure 849117DEST_PATH_IMAGE097
The number of the included slope section adjusting points is,
Figure 892159DEST_PATH_IMAGE098
is a chord length
Figure 966295DEST_PATH_IMAGE097
The number of the included vertical curve adjusting points is,
Figure 727577DEST_PATH_IMAGE099
is a chord length
Figure 181080DEST_PATH_IMAGE077
The number of included slope section adjusting points;
Figure 344208DEST_PATH_IMAGE100
is a chord length
Figure 589244DEST_PATH_IMAGE077
The number of the included vertical curve adjusting points;
Figure 103402DEST_PATH_IMAGE101
adjustment of fastener for slope adjustment point
Figure 92087DEST_PATH_IMAGE102
Adjustment of fastener to vertical curve adjustment point
Figure 109722DEST_PATH_IMAGE103
Corresponding coefficient matrix with number of rows
Figure 791239DEST_PATH_IMAGE104
The number of columns of the coefficient matrix is
Figure 323851DEST_PATH_IMAGE105
；
Figure 991593DEST_PATH_IMAGE106
Adjustment of fastener for slope adjustment point
Figure 988368DEST_PATH_IMAGE107
Adjustment of fastener to vertical curve adjustment point
Figure 716152DEST_PATH_IMAGE103
Corresponding constraint matrix with row number of
Figure 63957DEST_PATH_IMAGE104
The number of columns is 1;
Figure 269810DEST_PATH_IMAGE108
a fastener adjustment matrix for the slope and vertical curve adjustment points, the number of rows of the fastener adjustment matrix being
Figure 386671DEST_PATH_IMAGE105
The number of columns is 1;
solving the matrix inequality according to an optimization theory, calculating to obtain the fastener adjustment quantity of the slope section adjustment point and the vertical curve adjustment point of the whole section of the circuit, wherein the calculation result meets the constraint of the fastener adjustment quantity, and a fastener adjustment quantity optimization scheme is formulated.
5. The ballastless track smoothness control method for the pier settlement section of claim 4, wherein the step C specifically comprises:
c-1, guiding constructors to accurately adjust the reference rail by adopting a fastener adjustment quantity optimization scheme in a ballastless track of a bridge pier settlement section, measuring internal geometric parameters of the track after the reference rail is adjusted to a correct position, and adjusting a non-reference rail according to the internal geometric parameters, wherein the internal geometric parameters of the track comprise: gauge, gauge rate of change, level and twist;
and C-2, after the first operation is finished, acquiring track irregularity information after fine adjustment by using a track inspection instrument, evaluating the implementation effect of the fastener adjustment optimization scheme in the first operation process, adjusting the design parameters of the longitudinal section in the step A according to the adaptability of the scheme to the integral deviation of the pier settlement section, adjusting the constraint control conditions in the step B according to the improvement capability of the scheme to the periodic track irregularity, recalculating the fastener adjustment of the remaining line to be adjusted, and obtaining the final fastener adjustment optimization scheme.
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