CN117708961A - Integrated intelligent reconstruction method for three-dimensional space line position of existing railway - Google Patents
Integrated intelligent reconstruction method for three-dimensional space line position of existing railway Download PDFInfo
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Abstract
The invention relates to the technical field of railway design, in particular to an integral intelligent reconstruction method of an existing railway three-dimensional space line position, which comprehensively considers the mutual influence between plane design and longitudinal plane design, provides an optimization variable for integral reconstruction of the existing railway three-dimensional space line position and an objective function for evaluating an optimal scheme, provides constraint conditions for controlling the optimization direction, provides a progressive update strategy for three-dimensional space line position optimization of a line, and adopts a particle swarm algorithm mixed grid adaptive direct search algorithm (PSO-MADS mixed algorithm) to obtain an optimal three-dimensional space line position integral reconstruction scheme by combining the constraint conditions; compared with a two-dimensional independent reconstruction method, the scheme obtained by applying the reconstruction method provided by the invention is used for railway reconstruction and reconstruction, so that the cost can be reduced.
Description
Technical Field
The invention relates to the technical field of railway design, in particular to an integral intelligent reconstruction method for three-dimensional space line positions of an existing railway.
Background
The abrasion and impact between the locomotive and the wheel rail during long-term running of the railway lead to the deviation of the railway line position from the original design, and influence the safety of the running of the railway, the comfort of passengers and the service life of the railway. Therefore, the problem of increasing and rebuilding the existing railway is a key problem faced by railway construction, and the research on the reconstruction method of the railway line position is particularly important for increasing and rebuilding the existing railway.
The existing railway is a three-dimensional line in space, the current line reconstruction method focuses on two-dimensional design with independent plane or longitudinal plane, when plane line reconstruction is performed, the intersection point coordinates, the radius of the curve and the slow length are adjusted, the sum of squares of track pulling amounts of the plane line is used as a design target, when the longitudinal section line reconstruction is performed, the sum of squares of lifting track lifting amounts of the line is used as a target, the position (mileage and elevation of the variable slope point) of the variable slope point and the radius of the vertical curve are optimized, and the longitudinal plane optimization is generally performed after the plane design is completed. Because of the mutual influence between the line plane and the longitudinal plane design, only plane constraint conditions are considered and longitudinal plane constraint conditions are ignored when the line plane is independently subjected to the reconstruction design, the finished plane design can limit the subsequent longitudinal plane reconstruction design, a better longitudinal plane scheme cannot be generated, and then the final reconstruction scheme cannot achieve the overall optimal three-dimensional space line position, so that the existing railway has over-high reconstruction cost.
Based on the above, in order to ensure that the three-dimensional space line position is integrally optimal during line reconstruction, the existing railway reconstruction cost is reduced, and an existing railway three-dimensional space line position integrally intelligent reconstruction method is urgently needed.
Disclosure of Invention
The invention aims to provide an integral intelligent reconstruction method for the three-dimensional space line position of the existing railway, which considers the mutual influence between planar line shape and longitudinal section line position design and solves the problem that the final scheme cannot achieve integral optimization of the three-dimensional line position because the existing method only carries out reconstruction optimization on planar and longitudinal surfaces singly.
The technical scheme adopted by the invention is as follows:
an existing railway three-dimensional space line position integral intelligent reconstruction method comprises the following steps:
the design variables of the three-dimensional line to be reconstructed are determined, specifically: taking the intersection point coordinates of the line plane, the length of the moderation curve, the radius of the circular curve, the distance of the slope change point of the longitudinal surface, the elevation of the slope change point and the radius of the vertical curve as optimization variables;
the objective function is determined, specifically: taking the minimum sum of the square sum of the track shifting quantity of the line plane and the square sum of the track lifting quantity of the longitudinal plane as an objective function;
calculating the distance from the measuring point to the reconstructed line plane projection point; calculating the distance from the measuring point to the reconstructed line longitudinal plane projection point;
determining constraint conditions, specifically: determining constraint conditions to be met when the line is reconstructed and designed, wherein the constraint conditions comprise plane constraint, longitudinal plane constraint, cross section constraint and complex association constraint of the line-structure;
The method for acquiring the initial three-dimensional line scheme comprises the following steps: calculating the azimuth angle change rate and the longitudinal slope change rate of the plane curve measuring point, and primarily dividing the attribution of the measuring point line element based on the azimuth angle and the slope change rate of the measuring point; after the line elements are primarily divided, fitting straight lines and curves of a flat plane and a longitudinal plane, oscillating and iterating, and precisely dividing the attribution of the line elements to obtain an initial three-dimensional line scheme;
based on design variables, objective functions, constraint conditions, distances from measuring points to the reconstructed line plane projection points, distances from measuring points to the reconstructed line longitudinal plane projection points and an initial three-dimensional line scheme of the three-dimensional line to be reconstructed, a particle swarm algorithm mixed grid self-adaptive direct search algorithm (PSO-MADS mixed algorithm) is adopted to progressively optimize an initial particle swarm, so that an optimal solution of the line scheme is obtained, and the integral intelligent reconstruction of the existing railway three-dimensional space line position is realized.
Further, the design variables for determining the three-dimensional line to be reconstructed are specifically:
the intersection point coordinates, the front relaxation curve length, the rear relaxation curve length, the circle curve radius, the slope-changing point mileage of the longitudinal surface and the slope-changing point elevation and the vertical curve radius of the line plane are used as optimization variables, and the total number of plane intersection points of the whole line is set as The total number of the slope points is +.>The three-dimensional space line bits of the line to be optimized are represented by the following vectors:
intersection pointCoordinate column vector: />；
Intersection pointCoordinate column vector: />；
Front relaxation curve length column vector:；
circular curve radius column vector:；
post-relaxation curve length column vector:；
slope change point mileage column vector:；
slope change point Gao Chenglie vector:；
vertical curve radius column vector:。
further, the minimum sum of the square sum of the track shifting quantity of the line plane and the square sum of the track lifting quantity of the longitudinal plane is taken as an objective function, and expressed by a formula 1):
1）；
in formula 1):
representing the field actual measurement point set->；
Representing the line column vector of the existing railway three-dimensional space;
indicating measuring point->Distance to the reconstructed line projection point;
a function representing the calculated measurement point adjustment;
a function for calculating the adjustment quantity of the planar linear measuring point;
the function of calculating the adjustment amount of the longitudinal line position measuring point is shown.
Further, the distance (i.e. plane adjustment amount) from the measurement point to the reconstructed line plane projection point is specifically:
the line plane line element is divided into a linear line element, a circular curve line element and a buffer curve line element, and plane adjustment amounts of the linear line element, the circular curve line element and the buffer curve line element are calculated respectively;
(1) Linear line element
Let the fitted linear equation beMeasuring point on straight line element->The plane adjustment amount of (2) is:
2）；
(2) Circular curve line element
Let the fitted round curve equation beThen the measuring point on the circular curve line element is +.>The plane adjustment amount of (2) is:
3）；
in the formula 3), the amino acid sequence of the formula (III),center coordinates of a curve equation of a reconstructed plane circle, < ->Radius of the reconstructed plane circular curve;
(3) Moderating curve line element
For the relaxation curve, the planar adjustment amount is calculated iteratively by adopting a dichotomy: set round slow pointTangential line and measuring pointThe included angle of the connecting line is->Straight-line point->Tangential line and measuring point->The included angle of the connecting line is->Selecting the position of the midpoint of the moderation curve +.>If->The included angle between the tangential line and the measuring point connecting line is equal to +.>Or less than the set threshold, stopping the iteration, < ->To->Distance of->The plane adjustment quantity of the measuring point is obtained; otherwise, byAnd continuing iteration for alleviating the curve end point until the iteration termination condition is met.
Further, the distance (i.e. the lifting channel amount) from the measuring point to the reconstructed line longitudinal plane projection point is specifically:
the line longitudinal line element is divided into a linear line element and a vertical curve line element, and the lifting channel quantity of the linear line element and the vertical curve line element, namely the longitudinal surface adjustment quantity, is calculated respectively;
(1) Linear line element
Let the linear element equation of the reconstructed longitudinal plane be Then straight line part measuring point ∈ ->The lifting and falling path amount (namely, the adjustment amount) is as follows:
4）；
in the formula 4), the amino acid sequence of the formula,slope of straight line equation of reconstructed longitudinal slope, i.e. reconstructed straight line slope, +.>Reconstructing the intercept of a longitudinal slope linear equation;
(2) Vertical curve line element
Let the curve equation of the vertical curve beThen the measuring point is located within the vertical curve>Is->The method comprises the following steps:
5）；
in the formula 5), the amino acid sequence of the formula,the center coordinates of the vertical curve of the reconstruction longitudinal surface are reconstructed; />Radius of the vertical curve of the reconstructed longitudinal surface.
Further, constraint conditions are determined, specifically:
constraint conditions to be met during line reconstruction are determined, wherein the constraint conditions comprise plane constraint, longitudinal plane constraint, cross section constraint and complex association constraint of a line-structure, and the constraint conditions specifically comprise:
(1) Plane constraint
6）；
In the formula 6), the amino acid sequence of the formula,is the minimum circle curve length of the plane->For clamping the straight line length->Is a slow dot->To the gentle circle point->Is (are) corner of (are)>Reconstructing the curve radius of the line plane, < >>To mitigate the curve length;
(2) Longitudinal plane restraint
7）；
In the formula (7), the amino acid sequence of the formula (I),for the length of the slope section between adjacent slope changing points, < > and->Is the maximum allowable descending gradient +.>Is the maximum allowable ascending slope +.>Is the algebraic difference of the gradient of adjacent slope segments +.>Is the algebraic difference of maximum gradient>Is the radius of a vertical curve;
(3) Cross-sectional constraint
The amount of movement of the cross section caused by the line plane and longitudinal plane adjustment amounts does not exceed the limit range, expressed as:
8）；
in the formula 8), the amino acid sequence of the formula (I),to calculate the function of the movement of the cross section +.>For the gradient of roadbed>Is the gradient of embankment or cutting +.>Distance from roadbed to limit;
(4) Line-structure complex association constraints
The longitudinal line surface should ensure that the vertical curve part does not overlap with the relief curve, the bridge and the switch, expressed as:
9）；
formula 9):
representation ofFirst->Starting mileage of each flat curve>Indicate->End mileage of each flat curve>Indicate->Starting mileage of each vertical curve>Indicate->End mileage of each vertical curve;
the amount of site adjustment for which there is a limit to the engineering structure should meet the allowable adjustment amount requirement, expressed as:
10）；
in the formula 10), the amino acid sequence of the formula,for the minimum left adjustment of the measuring point, +.>For maximum adjustment of the measuring point to the right, +.>For the minimum adjustment of the measuring point upwards, +.>The measurement point is the maximum adjustment amount downwards.
Further, the obtaining of the initial three-dimensional line scheme specifically includes:
calculating azimuth angle change rate of the plane curve measuring point, and primarily distinguishing plane line element attribution;
according to the measuring pointsCoordinates and mileage of (2) and finding the measuring point +.>Azimuth change rate +.>Specifically, the method comprises the steps of,
11）；
in the formula (11), the amino acid sequence of the formula (11), For measuring points->Azimuth angle of->For measuring points->Is a mileage of (1);
calculating measuring points in sequenceAnd->Azimuth angle change rate of 1 st measuring point is 0, +.>The azimuth angle change rate of each measuring point is equal to +.>Azimuth angle change rates of the measuring points; let the maximum allowable curve radius of the line be +.>Consider->The measuring points belong to the linear line element parts, and the rest measuring points belong to the curve line element parts;
calculating the change rate of the slope of the longitudinal surface, and primarily distinguishing the attribution of the longitudinal surface line elements;
according to the measuring pointsCoordinates and mileage of (2) and finding the measuring point +.>Slope change rate +.>Specifically, the method comprises the steps of,
12）；
in the formula 12), the amino acid sequence of the formula,for measuring points->Elevation of->For measuring points->Is a slope of (2);
calculating measuring points in sequenceAnd->The gradient change rate of the 1 st measuring point is 0, the +.>The gradient change rate of each measuring point is equal to +.>Slope change rates of the measuring points; the gradient change rate of the straight line slope tends to 0, the gradient change rate of the vertical curve tends to the reciprocal of the radius of the vertical curve, and the minimum radius of the vertical curve is set as +.>Then consider the gradient change rate +>Less than->When the threshold value is reached, the measuring points belong to the straight slope line element part, and the rest measuring points belong to the vertical curve part;
and fitting the straight line and the curve of the plane and the longitudinal plane by using a least square method and constraint conditions according to the primary dividing result of the line element attribution, dividing the straight line and the curve line element attribution again based on the primary fitting result, fitting for the second time according to the secondary dividing result, and oscillating and iterating until the line element attribution dividing result is not changed or reaches the maximum iteration times, thus obtaining the initial three-dimensional line shape of the line.
Furthermore, the realization of the integral intelligent reconstruction of the three-dimensional space line position of the existing railway is specifically as follows: generating an initial particle swarm in a line feasible search domain by utilizing normal distribution on the basis of an initial three-dimensional line scheme, and performing progressive optimization on the initial particle swarm based on a PSO-MADS hybrid algorithm to obtain an optimal solution of the line scheme;
the method specifically comprises the following steps:
step S1, generating a feasible search domain in a certain range near an initial line according to a formed initial line scheme;
s2, taking an initial scheme as an expectation, and randomly generating an initial particle swarm in a feasible search domain based on normal distribution;
step S3, traversing particle swarms based on a PSO algorithm, calculating individual fitness values, updating individual optimal positions and global optimal positions, and further updating plane line related parameters; optimizing plane line related parameters based on MADS algorithm; optimizing longitudinal parameters based on a PSO algorithm;
and S4, repeating the step S3, iteratively updating the initial three-dimensional line scheme, calculating an objective function value of the updated scheme according to the objective function, updating an individual optimal solution and a global optimal solution of the particle swarm, and continuing iteration until the iteration times reach the maximum iteration times, thus obtaining the optimal three-dimensional space integral line-position scheme.
Further, the PSO-MADS hybrid algorithm is realized according to the following principle:
initializing a scheme in a PSO algorithm (namely a particle swarm algorithm) into a group of random particles in a vector space, iterating according to a formula 13 to obtain the optimal position of the particles and the optimal position of the population, updating an initial particle swarm, and determining the dimension of the vector space by the number of variables;
13）；
formula 13):
is->Particle->The velocity vector after the number of iterations,
is->Particle->The position vector after the number of iterations,
is->The initial position vector of the individual particles,
is->Particle->The optimal position of the individual is iterated for a number of times,
is->The initial optimal position of the individual particles is equal to +.>，
Is the global optimum position of the particle swarm,
for a globally optimal position of the initial population of particles,
as the weight of the inertia is given,
in order for the acceleration constant to be high,
is [0,1]Random numbers within the range;
in MADS algorithm (i.e. grid self-adaptive direct search algorithm), searching for radius and length of plane circle curve in variable and objective function of search point in set grid setAnd evaluating, and obtaining an optimal solution by continuously and iteratively searching the descending direction and the step length.
Grid adaptive direct search algorithm (MADS algorithm) is updated by particle swarm algorithm The corresponding vectors (the radius of the plane circular curve and the length of the moderation curve) are initial values, the initial grid search sizes of the radius of the plane circular curve and the length of the moderation curve are respectively set, test points are sequentially selected on the grid, the function values of the test points are calculated according to the objective function F, the function values of the test points are compared with the function values of the previous grid points, whether the search is successful or not is evaluated according to the comparison result, whether a polling process is executed or not is determined according to the search result, the grid search size is reduced or enlarged according to the search or polling result, and the optimal solution is continuously searched and updated until the grid size reaches a set value.
Further, the step S1 specifically includes:
obtaining accurate intersection points and variable slope points according to an initial scheme, and calculating the measurement in the range of each intersection point in a plane lineCalculating the track lifting and falling quantity of measuring points in each slope changing point range in the longitudinal line according to the track lifting quantity from the point to the reconstruction line, and taking the maximum values of the plane track lifting quantity and the longitudinal track lifting and falling quantity as follows respectivelyAnd->The method comprises the steps of carrying out a first treatment on the surface of the Calculating the adjustment amounts of each intersection point and the slope change point range under the constraint condition by combining the constraint condition, and taking the minimum values of the adjustment amounts as +.>And->The method comprises the steps of carrying out a first treatment on the surface of the If there is a control constraint in the range of each intersection and slope change point, the planar feasible search domain bandwidth is +. >The longitudinal surface is->The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, the planar feasible search domain bandwidth is +.>The longitudinal surface is->；
The step S2 specifically comprises the following steps:
obtaining initial values of intersection point coordinates, slope change point mileage and slope change point elevation based on random change of normal distribution in a feasible search domain, and fitting a vertical curve radius meeting constraint conditions; taking the minimum square sum of the track dialing quantities of the plane measuring points in the intersection point range as a target, and optimizing the radius of the plane circular curve and the length of the moderation curve by using an MADS algorithm in combination with constraint conditions to obtain initial particles; regenerating if the initial particles do not meet the constraint condition, and continuously repeating the process until initial particle groups meeting the condition are generated;
the step S3 specifically comprises the following steps:
(1) Calculating fitness of each particle according to formula 1) to obtain individual optimal solutions of the particlesAdopting formula 13) to iteratively update the speed variable and the position variable, calculating the fitness value of all real measurement points of the line scheme represented by the position variable, and if the iterative particle fitness is better than the individual optimal solution +.>Updating the individual optimal solution; if->Better than global optimal solution->Then the globally optimal solution is updated to +.>Based on the individual optimal position->And->Updating the related parameters of the particle plane circuit;
(2) Optimizing the radius and the moderation length of the plane circular curve by adopting MADS algorithm, and setting iteration countThe initial point is +.>Objective function->Expressed as:
14）；
in the formula 14), the amino acid sequence of the formula,is a measuring point set in the range of plane intersection points;
the method is set by considering the difference of the radius of the circular curve and the variation range of the length of the curveIs 100m,/c>Is 10m;
the function value of each point is calculated according to formula 14) in the grid search process, if a new grid point is presentThen the search is successful, the optimal solution is updated>Simultaneously updating the parameter->For the next iteration; otherwise, turning to a polling process, estimating an objective function of points in the adjacent range of the current grid point, and if a new grid point objective function value is found to be better than the current grid point, updating the optimal solution +.>Update parameter->The method comprises the steps of carrying out a first treatment on the surface of the If no new grid point is found to be better than the current grid point, carrying out optimizing search on other grid point sets in a certain field of the grid point set generated in the polling process;
if no better solution is found in the searching and polling processes, the method comprises the steps ofUpdate parameter->And reduce the grid size, search for localA better solution; if a better solution is generated in the searching and polling processes, updating the current optimal solution, and maintaining or expanding grid size parameters to quickly search the global optimal solution until the grid size reaches a set value, namely stopping searching; when the constraint condition is processed by the MADS algorithm, the minimum circle curve radius and the minimum relaxation curve length are used as insurmountable constraint, in the searching process, whether the grid point meets the insurmountable constraint condition is judged, if not, the grid point is abandoned, and whether the next grid point meets the constraint condition is continuously judged; the allowable adjustment quantity of the major structure is regarded as surmountable constraint, and in the searching process, if the grid points do not meet the surmountable constraint condition, the allowable adjustment quantity is adaptively reduced in the iterative process until solutions meeting all control point constraints are searched out;
(3) PSO algorithm is adopted and based onAnd->Updating related parameters of the longitudinal line scheme, and ensuring that the parameters meet all constraint conditions; setting a moderation curve, a positive line turnout and a bright bridge deck as a vertical curve forbidden zone, and calculating the minimum vertical curve length according to a formula 15) under the condition that the variable slope point is far enough from the vertical curve forbidden zone to ensure the shortest vertical curve length:
15）；
slope point change mileage when vertical curve length is minimumAnd nearest feature point->Point and->Mileage difference ∈10 between points>Equation 16) should be satisfied:
16）；
in the formula 16), the amino acid sequence of the formula,connecting line corner for adjacent slope changing points>Half of (2);
obtaining the mileage range of the variable slope point according to the formula 16), adopting a speed update formula and a position update formula in the formula 13), and updating the mileage of the variable slope point once by combining constraint conditionsThe method comprises the steps of carrying out a first treatment on the surface of the The position of the slope change point after updating is +.>From equations 15), 16):
17）；
front-rear gradient of slope changing point：
18）；
Solving inequalities 17) and 18) to find the elevation of the slope pointIs used for updating the primary slope change point elevation in the range by combining the constraint condition and the speed update formula and the position update formula of the formula 13)>The method comprises the steps of carrying out a first treatment on the surface of the At this time->And->It is known that the vertical curve radius is updated according to the velocity update formula and the position update formula of inequality 17) and formula 13).
The technical scheme of the invention has the following beneficial effects:
(1) The invention comprehensively considers the mutual influence between the plane design and the longitudinal plane design, provides an optimization variable for the integral reconstruction of the three-dimensional space line and the objective function for evaluating the optimal scheme of the existing railway, provides a constraint condition for controlling the optimization direction, provides a progressive update strategy for the three-dimensional space line and the position optimization of the line, adopts a particle swarm algorithm mixed grid self-adaptive direct search algorithm (PSO-MADS mixed algorithm) and combines the constraint condition to obtain the optimal three-dimensional space line and position integral reconstruction scheme; compared with a two-dimensional independent reconstruction method, the scheme obtained by applying the reconstruction method provided by the invention is used for railway reconstruction and reconstruction, and the cost is reduced.
(2) The invention comprehensively considers plane constraint, longitudinal plane constraint, cross section constraint and complex association constraint conditions of the circuit-structure object during the integral reconstruction of the three-dimensional space line position of the circuit, and ensures that the reconstruction scheme meets the circuit specification.
(3) The invention provides an optimization model and a progressive updating strategy based on a particle swarm algorithm hybrid grid self-adaptive direct search algorithm, which are convenient for optimizing an initial particle swarm by using a computer, searching an optimal scheme and improving the optimization speed.
In addition to the objects, features and advantages described above, the present invention has other objects, features and advantages. The present invention will be described in further detail with reference to the drawings.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention. In the drawings:
FIG. 1 is a flow chart of the general steps of the present invention;
FIG. 2 is a flow chart for generating an initial three-dimensional line bit scheme;
FIG. 3 is a schematic diagram of a station group divided by line elements of a line plane;
FIG. 4 is a schematic diagram of a station group divided by line longitudinal line elements;
FIG. 5 is a diagram of a dichotomy iterative calculation of the adjustment amount of the measurement point of the element range of the relaxation curve;
FIG. 6 is a schematic diagram of a vertical curve;
FIG. 7 is a flowchart of the steps for optimizing a three-dimensional wiring scheme based on the PSO-MADS algorithm.
Detailed Description
Embodiments of the invention are described in detail below with reference to the attached drawings, but the invention can be implemented in a number of different ways, which are defined and covered by the claims.
Examples
Referring to fig. 1, the embodiment provides a method for integrally and intelligently reconstructing three-dimensional space line positions of an existing railway, which comprises the following steps:
Determining design variables of a three-dimensional line to be reconstructed, and taking intersection point coordinates, a moderation curve length, a round curve radius, a slope change point mileage of a longitudinal surface, a slope change point elevation and a vertical curve radius of a line plane as optimization variables;
specifically, the intersection point coordinates, the front relaxation curve length, the rear relaxation curve length, the radius of a circular curve, the distance of a variable slope point of a longitudinal surface, the elevation of the variable slope point and the radius of a vertical curve of a longitudinal surface are taken as optimization variables, and the total number of plane intersection points of the whole line is set asThe total number of the slope points is +.>The three-dimensional space line bits of the line to be optimized are represented by the following vectors:
intersection pointCoordinate column vector: />；
Intersection pointCoordinate column vector: />；
Front relaxation curve length column vector:；
circular curve radius column vector:；
post-relaxation curve length column vector:；
slope change point mileage column vector:；
slope change point Gao Chenglie vector:；
vertical curve radius column vector:。
determining an objective function, wherein the minimum sum of the square sum of the track shifting quantity of the line plane and the square sum of the track lifting quantity of the longitudinal plane is taken as the objective function, and the objective function is expressed by a formula 1):
1）；
in formula 1):
representing the field actual measurement point set->；
Representing the line column vector of the existing railway three-dimensional space;
indicating measuring point->Distance to the reconstructed line projection point;
A function representing the calculated measurement point adjustment;
a function for calculating the adjustment quantity of the planar linear measuring point;
the function of calculating the adjustment amount of the longitudinal line position measuring point is shown.
The distance (namely plane adjustment quantity) from the measuring point to the reconstructed line plane projection point is calculated, and specifically:
the line plane line element is divided into a linear line element, a circular curve line element and a buffer curve line element, and plane adjustment amounts of the linear line element, the circular curve line element and the buffer curve line element are calculated respectively;
(1) Linear line element
Let the fitted linear equation beMeasuring point on straight line element->The plane adjustment amount of (2) is:
2）；
(2) Circular curve line element
Let the fitted round curve equation beThen the measuring point on the circular curve line element is +.>The plane adjustment amount of (2) is:
3）；
in the formula 3), the amino acid sequence of the formula (III),center coordinates of a curve equation of a reconstructed plane circle, < ->Radius of the reconstructed plane circular curve;
(3) Moderating curve line element
For the relaxation curve, the planar adjustment amount is calculated iteratively by adopting a dichotomy: set round slow pointTangential line and measuring pointThe included angle of the connecting line is->Straight-line point->Tangential line and measuring point->The included angle of the connecting line is->Selecting the position of the midpoint of the moderation curve +.>If->The included angle between the tangential line and the measuring point connecting line is equal to +.>Or less than the set threshold, stopping the iteration, < - >To->Distance of->The plane adjustment quantity of the measuring point is obtained; otherwise, to beThe relaxation curve end point continues the iteration until the iteration termination condition is met, see fig. 5.
The distance (namely the lifting and falling channel quantity) from the measuring point to the reconstructed line longitudinal plane projection point is calculated, and specifically:
the line longitudinal line element is divided into a linear line element and a vertical curve line element, and the lifting channel quantity of the linear line element and the vertical curve line element, namely the longitudinal surface adjustment quantity, is calculated respectively;
(1) Linear line element
Let the linear element equation of the reconstructed longitudinal plane beThen straight line part measuring point ∈ ->The lifting and falling road quantity is as follows:
4）；
in the formula 4), the amino acid sequence of the formula,slope of straight line equation of reconstructed longitudinal slope, i.e. reconstructed straight line slope, +.>Reconstructing the intercept of a longitudinal slope linear equation;
(2) Vertical curve line element
Let the curve equation of the vertical curve beThen the measuring point is located within the vertical curve>The adjustment amount of (2) is->：
5）；
In the formula 5), the amino acid sequence of the formula,the center coordinates of the vertical curve of the reconstruction longitudinal surface are reconstructed; />Radius of the vertical curve of the reconstructed longitudinal surface.
Determining constraint conditions, specifically: constraint conditions to be met when the line reconstruction design is determined, including plane constraint, longitudinal plane constraint, cross section constraint and complex association constraint of the line-structure, specifically:
(1) Plane constraint
6）；
In the formula 6), the amino acid sequence of the formula, Is the minimum circle curve length of the plane->For clamping the straight line length->Is a slow dot->To the gentle circle point->Is (are) corner of (are)>Reconstructing the curve radius of the line plane, < >>To mitigate the curve length;
(2) Longitudinal plane restraint
7）；
In the formula (7), the amino acid sequence of the formula (I),for the length of the slope section between adjacent slope changing points, < > and->Is the maximum allowable descending gradient +.>Is the maximum allowable ascending slope +.>Is the algebraic difference of the gradient of adjacent slope segments +.>Is the algebraic difference of maximum gradient>Is the radius of a vertical curve;
(3) Cross-sectional constraint
The amount of movement of the cross section caused by the line plane and longitudinal plane adjustment amounts does not exceed the limit range, expressed as:
8）；
in the formula 8), the amino acid sequence of the formula (I),to calculate the function of the movement of the cross section +.>For the gradient of roadbed>Is the gradient of embankment or cutting +.>Distance from roadbed to limit;
(4) Line-structure complex association constraints
The longitudinal line surface should ensure that the vertical curve part does not overlap with the relief curve, the bridge and the switch, expressed as:
9）；
formula 9):
indicate->Starting mileage of each flat curve>Indicate->End mileage of each flat curve>Indicate->Starting mileage of each vertical curve>Indicate->End mileage of each vertical curve;
the amount of site adjustment for which there is a limit to the engineering structure should meet the allowable adjustment amount requirement, expressed as:
10）；
In the formula 10), the amino acid sequence of the formula,for the minimum left adjustment of the measuring point, +.>For maximum adjustment of the measuring point to the right, +.>For the minimum adjustment of the measuring point upwards, +.>The measurement point is the maximum adjustment amount downwards.
Acquisition of an initial three-dimensional line plan, see fig. 2, specifically: calculating the azimuth angle change rate and the longitudinal slope change rate of the plane curve measuring point, and primarily dividing the attribution of the measuring point line element based on the azimuth angle and the slope change rate of the measuring point; after the line elements are primarily divided, fitting straight lines and curves of a flat plane and a longitudinal plane, oscillating and iterating, and precisely dividing the attribution of the line elements to obtain an initial three-dimensional line scheme;
specific:
calculating azimuth angle change rate of the plane curve measuring point, and primarily distinguishing plane line element attribution;
according to the measuring pointsCoordinates and mileage of (2) and finding the measuring point +.>Azimuth change rate +.>Specifically, the method comprises the steps of,
11）；
in the formula (11), the amino acid sequence of the formula (11),for measuring points->Azimuth angle of->For measuring points->Is a mileage of (1);
calculating measuring points in sequenceAnd->Azimuth angle change rate of 1 st measuring point is 0, +.>The azimuth angle change rate of each measuring point is equal to +.>Azimuth angle change rates of the measuring points; let the maximum allowable curve radius of the line be +.>Consider->The time measuring points belong to the linear line element part, and the rest measuring points belong to the curve line element part, see FIG. 3;
calculating the change rate of the slope of the longitudinal surface, and primarily distinguishing the attribution of the longitudinal surface line elements;
according to the measuring pointsCoordinates and mileage of (2) and finding the measuring point +.>Slope change rate +.>Specifically, the method comprises the steps of,
12）；
in the formula 12), the amino acid sequence of the formula,for measuring points->Elevation of->For measuring points->Is a slope of (2);
calculating measuring points in sequenceAnd->The gradient change rate of the 1 st measuring point is 0, the +.>The gradient change rate of each measuring point is equal to +.>Slope change rates of the measuring points; the gradient change rate of the straight slope tends to 0, and the gradient change rate of the vertical curve tends to the radius of the vertical curveReciprocal, setting minimum radius of vertical curve as +.>Then consider the gradient change rate +>Less than->The measuring point at this threshold belongs to the straight slope line element part, and the rest of the measuring points belong to the vertical curve part, see fig. 4;
and fitting the straight line and the curve of the plane and the longitudinal plane by using a least square method and constraint conditions according to the primary dividing result of the line element attribution, dividing the straight line and the curve line element attribution again based on the primary fitting result, fitting for the second time according to the secondary dividing result, and oscillating and iterating until the line element attribution dividing result is not changed or reaches the maximum iteration times, thus obtaining the initial three-dimensional line shape of the line.
Based on design variables, objective functions, constraint conditions, distances from measuring points to the reconstructed line plane projection points, distances from measuring points to the reconstructed line longitudinal plane projection points and an initial three-dimensional line scheme, generating initial particle swarms in a line feasible search domain by utilizing normal distribution, performing progressive optimization on the initial particle swarms based on a PSO-MADS hybrid algorithm to obtain an optimal solution of the line scheme, and realizing the integral intelligent reconstruction of the existing railway three-dimensional space line position.
The PSO-MADS hybrid algorithm is realized by the following principle:
initializing a scheme in a PSO algorithm (namely a particle swarm algorithm) into a group of random particles in a vector space, iterating according to a formula 13 to obtain the optimal position of the particles and the optimal position of the population, updating an initial particle swarm, and determining the dimension of the vector space by the number of variables;
13）；
formula 13):
is->Particle->The velocity vector after the number of iterations,
is->Particle->The position vector after the number of iterations,
is->The initial position vector of the individual particles,
is->Particle->Individual optimal position for next iteration, ->
Is->The initial optimal position of the individual particles is equal to +.>，
Is the global optimum position of the particle swarm,
for a globally optimal position of the initial population of particles,
as the weight of the inertia is given,
in order for the acceleration constant to be high,
is [0,1]Random numbers within the range;
in MADS algorithm (i.e. grid self-adaptive direct search algorithm), searching for radius and length of plane circle curve in variable and objective function of search point in set grid setAnd evaluating, and obtaining an optimal solution by continuously and iteratively searching the descending direction and the step length.
The grid self-adaptive direct search algorithm (MADS algorithm) takes vectors (a plane circle curve radius and a relaxation curve length) corresponding to positions updated by the particle swarm algorithm as initial values, the initial grid search size of the plane circle curve radius and the relaxation curve length is respectively set, test points are sequentially selected on the grid, the function values of the test points are calculated according to an objective function F, the function values are compared with the function values of the last grid point, whether the search is successful is evaluated according to the comparison result, whether a polling process is executed is determined according to the search result, the grid search size is reduced or enlarged according to the search or polling result, the optimal solution is continuously searched and updated until the grid size reaches a set value.
Referring to fig. 7, the specific steps for progressive optimization of the initial particle swarm based on the PSO-MADS hybrid algorithm are as follows:
step S1, generating a feasible search domain in a certain range near an initial line according to a formed initial line scheme;
s2, taking an initial scheme as an expectation, and randomly generating an initial particle swarm in a feasible search domain based on normal distribution;
step S3, traversing particle swarms based on a PSO algorithm, calculating individual fitness values, updating individual optimal positions and global optimal positions, and further updating plane line related parameters; optimizing plane line related parameters based on MADS algorithm; optimizing longitudinal parameters based on a PSO algorithm;
and S4, repeating the step S3, iteratively updating the initial three-dimensional line scheme, calculating an objective function value of the updated scheme according to the objective function, updating an individual optimal solution and a global optimal solution of the particle swarm, and continuing iteration until the iteration times reach the maximum iteration times, thus obtaining the optimal three-dimensional space integral line-position scheme.
The step S1 specifically comprises the following steps:
obtaining accurate intersection points and variable slope points according to an initial scheme, calculating the track shifting quantity from the measuring points in the range of each intersection point to the reconstruction line in a planar line, calculating the lifting track quantity of the measuring points in the range of each variable slope point in a longitudinal line, and taking the maximum values of the planar track shifting quantity and the longitudinal track lifting track quantity as follows respectively And->The method comprises the steps of carrying out a first treatment on the surface of the Calculating the adjustment amounts of each intersection point and the slope change point range under the constraint condition by combining the constraint condition, and taking the minimum values of the adjustment amounts as +.>And->The method comprises the steps of carrying out a first treatment on the surface of the If there is a control constraint in the range of each intersection and slope change point, the planar feasible search domain bandwidth is +.>The longitudinal surface is->The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, the planar feasible search domain bandwidth is +.>The longitudinal surface is->；
The step S2 specifically comprises the following steps:
obtaining initial values of intersection point coordinates, slope change point mileage and slope change point elevation based on random change of normal distribution in a feasible search domain, and fitting a vertical curve radius meeting constraint conditions; taking the minimum square sum of the track dialing quantities of the plane measuring points in the intersection point range as a target, and optimizing the radius of the plane circular curve and the length of the moderation curve by using an MADS algorithm in combination with constraint conditions to obtain initial particles; regenerating if the initial particles do not meet the constraint condition, and continuously repeating the process until initial particle groups meeting the condition are generated;
the step S3 specifically comprises the following steps:
(1) Calculating fitness of each particle according to formula 1) to obtain individual optimal solutions of the particlesAdopting formula 13) to iteratively update the speed variable and the position variable, calculating the fitness value of all real measurement points of the line scheme represented by the position variable, and if the iterative particle fitness is better than the individual optimal solution +. >Updating the individual optimal solution; if->Better than global optimal solution->Then the globally optimal solution is updated to +.>Based on the individual optimal position->And->Updating the related parameters of the particle plane circuit;
(2) Optimizing the radius and the moderation length of the plane circular curve by adopting MADS algorithm, and setting iteration countThe initial point is +.>Objective function->Expressed as:
14）；
in the formula 14), the amino acid sequence of the formula,is a measuring point set in the range of plane intersection points;
the method is set by considering the difference of the radius of the circular curve and the variation range of the length of the curveIs 100m,/c>Is 10m;
the function value of each point is calculated according to formula 14) in the grid search process, if a new grid point is presentThen the search is successful, the optimal solution is updated>Simultaneously updating the parameter->For the next iteration; otherwise, turning to a polling process, estimating an objective function of points in the adjacent range of the current grid point, and if a new grid point objective function value is found to be better than the current grid point, updating the optimal solution +.>Update parameter->The method comprises the steps of carrying out a first treatment on the surface of the If no new grid point is found to be better than the current grid point, carrying out optimizing search on other grid point sets in a certain field of the grid point set generated in the polling process;
if no better solution is found in the searching and polling processes, the method comprises the steps of Update parameter->Reducing the grid size, and searching for a local better solution; if a better solution is generated in the searching and polling processes, updating the current optimal solution, and maintaining or expanding grid size parameters to quickly search the global optimal solution until the grid size reaches a set value, namely stopping searching; when the constraint condition is processed by the MADS algorithm, the minimum circle curve radius and the minimum relaxation curve length are used as insurmountable constraint, in the searching process, whether the grid point meets the insurmountable constraint condition is judged, if not, the grid point is abandoned, and whether the next grid point meets the constraint condition is continuously judged; the allowable adjustment quantity of the major structure is regarded as surmountable constraint, and in the searching process, if the grid points do not meet the surmountable constraint condition, the allowable adjustment quantity is adaptively reduced in the iterative process until solutions meeting all control point constraints are searched out;
(3) PSO algorithm is adopted and based onAnd->Updating related parameters of the longitudinal line scheme, and ensuring that the parameters meet all constraint conditions; setting a moderation curve, a positive line turnout and a bright bridge deck as a vertical curve forbidden zone, and calculating the minimum vertical curve length according to a formula 15) under the condition that the variable slope point is far enough from the vertical curve forbidden zone to ensure the shortest vertical curve length:
15）；
Slope point change mileage when vertical curve length is minimumAnd nearest feature point->Point and->Mileage difference ∈10 between points>Equation 16) should be satisfied:
16）；
in the formula 16), the amino acid sequence of the formula,connecting line corner for adjacent slope changing points>See fig. 6; />
Obtaining the mileage range of the variable slope point according to the formula 16), adopting a speed update formula and a position update formula in the formula 13), and updating the mileage of the variable slope point once by combining constraint conditionsThe method comprises the steps of carrying out a first treatment on the surface of the The position of the slope change point after updating is +.>From equations 15), 16):
17）；
front-rear gradient of slope changing point：
18）；
Solving inequalities 17) and 18) to find the elevation of the slope pointIs used for updating the primary slope change point elevation in the range by combining the constraint condition and the speed update formula and the position update formula of the formula 13)>The method comprises the steps of carrying out a first treatment on the surface of the At this time->And->It is known that the vertical curve radius is updated according to the velocity update formula and the position update formula of inequality 17) and formula 13).
The following describes the technical scheme of the invention further by using the reconstruction case of the section line of the existing railway K133+400-K142+420 of the Portal-Changsha, wherein the section contains 472 measuring point data.
(1) And determining design variables, objective functions and constraint conditions of the line to be reconstructed.
Taking the intersection point coordinates of the line plane, the length of the moderation curve, the radius of the circular curve, the distance of the slope change point of the longitudinal surface, the elevation of the slope change point and the radius of the vertical curve as optimization variables;
Taking the minimum sum of the square sum of the track shifting quantity of the line plane and the square sum of the track lifting quantity of the longitudinal plane as an objective function;
calculating the distance from the measuring point to the projection point of the reconstructed line plane by sections (straight line section, circular curve section and gentle curve section);
calculating the distance from the measuring point to the projection point of the longitudinal plane of the reconstructed line by sections (straight line slope section and vertical curve slope section);
constraint conditions to be met in the process of line reconstruction design are determined, wherein the constraint conditions comprise plane constraint, longitudinal plane constraint, cross section constraint and line-structure complex association constraint. In the case, plane constraint and longitudinal plane constraint refer to line design standards, the control point limits the track shifting amount to 100mm, and limits the lifting track amount to 200mm.
(2) And (5) dividing the attribution of the measuring line element.
Calculating the azimuth angle change rate of each measuring point, and primarily dividing the attribution of the plane line elements of the measuring point according to the calculation result;
calculating the gradient and gradient change rate of each measuring point according to the mileage and the elevation of the measuring point, and primarily dividing the attribution of the longitudinal line element of the measuring point according to the calculation result;
fitting the straight curve element according to the primary line element dividing result by combining a least square method and constraint conditions, dividing the attribution of the straight curve element again based on the primary fitting result, fitting for the second time according to the re-dividing result, and oscillating and iterating until the line element attribution dividing result is not changed or reaches the maximum iteration times compared with the previous result, so as to obtain the initial three-dimensional line shape of the line.
(3) And performing progressive optimization on the initial particle swarm by adopting a particle swarm algorithm mixed grid self-adaptive direct search algorithm (PSO-MADS mixed algorithm) to obtain an optimal solution of the line scheme.
S1, generating a feasible search domain in a certain range near an initial line, and determining the bandwidth of the feasible search domain according to the plane track shifting quantity of a measuring point, the lifting and falling quantity of a longitudinal surface and the constraint of a control point;
s2, obtaining initial values of plane intersection point coordinates, slope change point mileage and slope change point elevation based on random change of normal distribution in a feasible search domain. Optimizing the radius of the plane circular curve and the length of the moderation curve by using the MADS algorithm and combining constraint conditions with the minimum sum of squares of track shifting amounts in the intersection point range as a target to obtain initial particles, and continuously repeating the process to obtain initial particle groups meeting the conditions;
s3, optimizing an initial particle swarm by using a PSO-MADS algorithm, calculating a particle fitness value, and updating according to a calculation resultAnd->；
And S4, repeating the step S3, iteratively updating the individual optimal solution and the global optimal solution of the particle swarm, and continuing iteration until the iteration times reach the maximum iteration times, thereby obtaining the optimal three-dimensional space line-position scheme.
In the reconstruction case, the total adjustment quantity of the scheme measuring points optimized according to the method is 0.61/m 2 The total adjustment quantity of the measurement points of the optimization scheme of the traditional two-dimensional horizontal and vertical separation type full line oscillation iteration method is 1.22/m 2 Compared with the traditional two-dimensional reconstruction method, the method has the advantages that the total adjustment amount of the measuring points is reduced, and therefore the line reconstruction cost is saved.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (10)
1. The intelligent reconstruction method for the three-dimensional space line position of the existing railway is characterized by comprising the following steps of:
the design variables of the three-dimensional line to be reconstructed are determined, specifically: taking the intersection point coordinates of the line plane, the length of the moderation curve, the radius of the circular curve, the distance of the slope change point of the longitudinal surface, the elevation of the slope change point and the radius of the vertical curve as optimization variables;
the objective function is determined, specifically: taking the minimum sum of the square sum of the track shifting quantity of the line plane and the square sum of the track lifting quantity of the longitudinal plane as an objective function;
calculating the distance from the measuring point to the reconstructed line plane projection point; calculating the distance from the measuring point to the reconstructed line longitudinal plane projection point;
Determining constraint conditions, specifically: determining constraint conditions to be met when the line is reconstructed and designed, wherein the constraint conditions comprise plane constraint, longitudinal plane constraint, cross section constraint and complex association constraint of the line-structure;
the method for acquiring the initial three-dimensional line scheme comprises the following steps: calculating the azimuth angle change rate and the longitudinal slope change rate of the plane curve measuring point, and primarily dividing the attribution of the measuring point line element based on the azimuth angle change rate and the slope change rate of the measuring point; after the line elements are primarily divided, fitting straight lines and curves of a flat plane and a longitudinal plane, oscillating and iterating, and precisely dividing the attribution of the line elements to obtain an initial three-dimensional line scheme;
based on design variables, objective functions, constraint conditions, distances from measuring points to the reconstructed line plane projection points, distances from measuring points to the reconstructed line longitudinal plane projection points and an initial three-dimensional line scheme of the three-dimensional line to be reconstructed, the particle swarm algorithm mixed grid self-adaptive direct search algorithm is combined to realize the integral intelligent reconstruction of the existing railway three-dimensional space line position.
2. The method for intelligently reconstructing the whole three-dimensional space line bit of the existing railway according to claim 1, wherein the design variables of the three-dimensional line to be reconstructed are determined specifically as follows:
the intersection point coordinates, the front relaxation curve length, the rear relaxation curve length, the circle curve radius, the slope-changing point mileage of the longitudinal surface and the slope-changing point elevation and the vertical curve radius of the line plane are used as optimization variables, and the total number of plane intersection points of the whole line is set as The total number of the slope points is +.>The three-dimensional space line bits of the line to be optimized are represented by the following vectors:
intersection pointCoordinate column vector: />；
Intersection pointCoordinate column vector: />；
Front relaxation curve length column vector:；
circular curve radius column vector:；
post-relaxation curve length column vector:；
slope change point mileage column vector:；
slope change point Gao Chenglie vector:；
vertical curve radius column vector:。
3. the method for intelligently reconstructing the line position of the three-dimensional space of the existing railway according to claim 1, wherein the sum of the square sum of the track lining quantity of the plane of the railway and the square sum of the track lifting quantity of the longitudinal plane is used as an objective function, and the method is expressed by the following formula 1):
1）；
in formula 1):
representing the field actual measurement point set->；
Representing the line column vector of the existing railway three-dimensional space;
indicating measuring point->Distance to the reconstructed line projection point;
a function representing the calculated measurement point adjustment;
a function for calculating the adjustment quantity of the planar linear measuring point;
the function of calculating the adjustment amount of the longitudinal line position measuring point is shown.
4. The method for intelligently reconstructing the line position of the three-dimensional space of the existing railway according to claim 1, wherein the distance from the measuring point to the reconstructed line plane projection point is calculated specifically as follows:
the line plane line element is divided into a linear line element, a circular curve line element and a buffer curve line element, and plane adjustment amounts of the linear line element, the circular curve line element and the buffer curve line element are calculated respectively;
(1) Linear line element
Let the fitted linear equation beMeasuring point on straight line element->The plane adjustment amount of (2) is:
2）；
(2) Circular curve line element
Let the fitted round curve equation beThen the measuring point on the circular curve line element is +.>The plane adjustment amount of (2) is:
3）；
in the formula 3), the amino acid sequence of the formula (III),center coordinates of a curve equation of a reconstructed plane circle, < ->Radius of the reconstructed plane circular curve;
(3) Moderating curve line element
For the relaxation curve, the planar adjustment amount is calculated iteratively by adopting a dichotomy: set round slow pointTangential line and measuring pointThe included angle of the connecting line is->Straight-line point->Tangential line and measuring point->The included angle of the connecting line is->Selecting the position of the midpoint of the moderation curve +.>If->The included angle between the tangential line and the measuring point connecting line is equal to +.>Or less than the set threshold, stopping the iteration, < ->To->Distance of->The plane adjustment quantity of the measuring point is obtained; otherwise, byAnd continuing iteration for alleviating the curve end point until the iteration termination condition is met.
5. The method for intelligently reconstructing the line position of the three-dimensional space of the existing railway according to claim 1, wherein the distance from the measuring point to the projection point of the longitudinal plane of the reconstructed line is calculated specifically as follows:
the line longitudinal line element is divided into a linear line element and a vertical curve line element, and the lifting channel quantity of the linear line element and the vertical curve line element, namely the longitudinal surface adjustment quantity, is calculated respectively;
(1) Linear line element
Let the linear element equation of the reconstructed longitudinal plane beThen straight line part measuring point ∈ ->The lifting and falling road quantity is as follows:
4）；
in the formula 4), the amino acid sequence of the formula,slope of straight line equation of reconstructed longitudinal slope, i.e. reconstructed straight line slope, +.>Reconstructing the intercept of a longitudinal slope linear equation;
(2) Vertical curve line element
Let the curve equation of the vertical curve beThe measuring point is located in the vertical curve rangeIs->The method comprises the following steps:
5）；
in the formula 5), the amino acid sequence of the formula,the center coordinates of the vertical curve of the reconstruction longitudinal surface are reconstructed; />Radius of the vertical curve of the reconstructed longitudinal surface.
6. The method for integrally intelligently reconstructing the three-dimensional space line bit of the existing railway according to claim 1, wherein the constraint conditions are determined specifically:
constraint conditions to be met during line reconstruction are determined, wherein the constraint conditions comprise plane constraint, longitudinal plane constraint, cross section constraint and complex association constraint of a line-structure, and the constraint conditions specifically comprise:
(1) Plane constraint
6）；
In the formula 6), the amino acid sequence of the formula,is the minimum circle curve length of the plane->For clamping the straight line length->Is a slow dot->To the gentle circle point->Is (are) corner of (are)>Reconstructing the curve radius of the line plane, < >>To mitigate the curve length;
(2) Longitudinal plane restraint
7）；
In the formula (7), the amino acid sequence of the formula (I),for the length of the slope section between adjacent slope changing points, < > and->Is the maximum allowable descending gradient +. >Is the maximum allowable ascending slope +.>Is the algebraic difference of the gradient of adjacent slope segments +.>Is the algebraic difference of maximum gradient>Is the radius of a vertical curve;
(3) Cross-sectional constraint
The amount of movement of the cross section caused by the line plane and longitudinal plane adjustment amounts does not exceed the limit range, expressed as:
8）；
in the formula 8), the amino acid sequence of the formula (I),to calculate the function of the movement of the cross section +.>For the gradient of roadbed>Is the gradient of embankment or cutting +.>Distance from roadbed to limit;
(4) Line-structure complex association constraints
The longitudinal line surface should ensure that the vertical curve part does not overlap with the relief curve, the bridge and the switch, expressed as:
9）；
formula 9):
indicate->Starting mileage of each flat curve>Indicate->End mileage of each flat curve>Indicate->Starting mileage of each vertical curve>Indicate->End mileage of each vertical curve;
the amount of site adjustment for which there is a limit to the engineering structure should meet the allowable adjustment amount requirement, expressed as:
10）；
in the formula 10), the amino acid sequence of the formula,for the minimum left adjustment of the measuring point, +.>For maximum adjustment of the measuring point to the right, +.>For the minimum adjustment of the measuring point upwards, +.>The measurement point is the maximum adjustment amount downwards.
7. The method for intelligent reconstruction of the existing railway three-dimensional space line bit entirety according to claim 1, wherein the obtaining of the initial three-dimensional line scheme is specifically:
Calculating azimuth angle change rate of the plane curve measuring point, and primarily distinguishing plane line element attribution;
according to the measuring pointsCoordinates and mileage of (2) and finding the measuring point +.>Azimuth change rate +.>Specifically, the method comprises the steps of,
11）；
in the formula (11), the amino acid sequence of the formula (11),for measuring points->Azimuth angle of->For measuring points->Is a mileage of (1);
calculating measuring points in sequenceAnd->Azimuth angle change rate of 1 st measuring point is 0, +.>The azimuth angle change rate of each measuring point is equal to +.>Azimuth angle change rates of the measuring points; let the maximum allowable curve radius of the line be +.>Then considerThe measuring points belong to the linear line element parts, and the rest measuring points belong to the curve line element parts;
calculating the change rate of the slope of the longitudinal surface, and primarily distinguishing the attribution of the longitudinal surface line elements;
according to the measuring pointsCoordinates and mileage of (2) and finding the measuring point +.>Slope change rate +.>Specifically, the method comprises the steps of,
12）；
in the formula 12), the amino acid sequence of the formula,for measuring points->Elevation of->For measuring points->Is a slope of (2);
calculating measuring points in sequenceAnd->The gradient change rate of the 1 st measuring point is 0, the +.>The gradient change rate of each measuring point is equal to +.>Slope change rates of the measuring points; the gradient change rate of the straight line slope tends to 0, the gradient change rate of the vertical curve tends to the reciprocal of the radius of the vertical curve, and the minimum radius of the vertical curve is set as +.>Then consider the gradient change rate + >Less than->When the threshold value is reached, the measuring points belong to the straight slope line element part, and the rest measuring points belong to the vertical curve part;
and fitting the straight line and the curve of the plane and the longitudinal plane by using a least square method and constraint conditions according to the primary dividing result of the line element attribution, dividing the straight line and the curve line element attribution again based on the primary fitting result, fitting for the second time according to the secondary dividing result, and oscillating and iterating until the line element attribution dividing result is not changed or reaches the maximum iteration times, thus obtaining the initial three-dimensional line shape of the line.
8. The method for integrally and intelligently reconstructing the three-dimensional space line position of the existing railway according to claim 1, wherein the implementation of the integrated and intelligent reconstruction of the three-dimensional space line position of the existing railway is specifically as follows: generating an initial particle swarm in a line feasible search domain by utilizing normal distribution on the basis of an initial three-dimensional line scheme, and performing progressive optimization on the initial particle swarm based on a PSO-MADS hybrid algorithm to obtain an optimal solution of the line scheme;
the method specifically comprises the following steps:
step S1, generating a feasible search domain in a certain range near an initial line according to a formed initial line scheme;
s2, taking an initial scheme as an expectation, and randomly generating an initial particle swarm in a feasible search domain based on normal distribution;
Step S3, traversing particle swarms based on a PSO algorithm, calculating individual fitness values, updating individual optimal positions and global optimal positions, and further updating plane line related parameters; optimizing plane line related parameters based on MADS algorithm; optimizing longitudinal parameters based on a PSO algorithm;
and S4, repeating the step S3, iteratively updating the initial three-dimensional line scheme, calculating an objective function value of the updated scheme according to the objective function, updating an individual optimal solution and a global optimal solution of the particle swarm, and continuing iteration until the iteration times reach the maximum iteration times, thus obtaining the optimal three-dimensional space integral line-position scheme.
9. The method for integrally intelligently reconstructing the three-dimensional space line bit of the existing railway according to claim 8, wherein the implementation principle of the PSO-MADS hybrid algorithm is as follows:
the scheme in the PSO algorithm is initialized to a group of random particles in a vector space, iteration is carried out according to a formula 13), the optimal positions of the particles and the optimal positions of the population are obtained, an initial particle swarm is updated, and the dimension of the vector space is determined by the number of variables;
13）；
formula 13):
is->Particle->The velocity vector after the number of iterations,
is->Particle->The position vector after the number of iterations,
Is->The initial position vector of the individual particles,
is->Particle->The optimal position of the individual is iterated for a number of times,
is->The initial optimal position of the individual particles is equal to +.>，
Is the global optimum position of the particle swarm,
for a globally optimal position of the initial population of particles,
as the weight of the inertia is given,
in order for the acceleration constant to be high,
is [0,1]Random numbers within the range;
in MADS algorithm, searching for radius and buffer curve length of plane circle curve in variable, and searching for objective function of search point in set grid setAnd evaluating, and obtaining an optimal solution by continuously and iteratively searching the descending direction and the step length.
10. The method for intelligent reconstruction of the three-dimensional space line bit of the existing railway according to claim 9, wherein the step S1 is specifically:
obtaining accurate intersection points and variable slope points according to an initial scheme, calculating the track shifting quantity from the measuring points in the range of each intersection point to the reconstruction line in a planar line, calculating the lifting track quantity of the measuring points in the range of each variable slope point in a longitudinal line, and taking the maximum values of the planar track shifting quantity and the longitudinal track lifting track quantity as follows respectivelyAnd->The method comprises the steps of carrying out a first treatment on the surface of the Calculating the adjustment amounts of each intersection point and the slope change point range under the constraint condition by combining the constraint condition, and taking the minimum values of the adjustment amounts as +.>And- >The method comprises the steps of carrying out a first treatment on the surface of the If there is control in each intersection point and slope change point rangeConstraint is made, the planar feasible search domain bandwidth is +.>The longitudinal surface is->The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, the planar feasible search domain bandwidth isThe longitudinal surface is->；
The step S2 specifically comprises the following steps:
obtaining initial values of intersection point coordinates, slope change point mileage and slope change point elevation based on random change of normal distribution in a feasible search domain, and fitting a vertical curve radius meeting constraint conditions; taking the minimum square sum of the track dialing quantities of the plane measuring points in the intersection point range as a target, and optimizing the radius of the plane circular curve and the length of the moderation curve by using an MADS algorithm in combination with constraint conditions to obtain initial particles; regenerating if the initial particles do not meet the constraint condition, and continuously repeating the process until initial particle groups meeting the condition are generated;
the step S3 specifically comprises the following steps:
(1) Calculating fitness of each particle according to formula 1) to obtain individual optimal solutions of the particlesAdopting formula 13) to iteratively update the speed variable and the position variable, calculating the fitness value of all real measurement points of the line scheme represented by the position variable, and if the iterative particle fitness is better than the individual optimal solution +.>Updating the individual optimal solution; if->Is superior to the global optimal solutionThen the globally optimal solution is updated to +. >Based on the individual optimal position->And->Updating the related parameters of the particle plane circuit;
(2) Optimizing the radius and the moderation length of a plane circular curve by adopting an MADS algorithm, and setting the grid point countThe initial point is +.>The objective function is expressed as:
14）；
in the formula 14), the amino acid sequence of the formula,is a measuring point set in the range of plane intersection points;
the method is set by considering the difference of the radius of the circular curve and the variation range of the length of the curveIs set to an initial mesh size of 100m,is 10m;
the function value of each point is calculated according to formula 14) in the grid search process, if a new grid point is presentThen the search is successful, the optimal solution is updated>Simultaneously updating the parameter->For the next iteration; otherwise, turning to a polling process, estimating an objective function of points in the adjacent range of the current grid point, and if a new grid point objective function value is found to be better than the current grid point, updating the optimal solution +.>Update parameter->The method comprises the steps of carrying out a first treatment on the surface of the If no new grid point is found to be better than the current grid point, carrying out optimizing search on other grid point sets in a certain field of the grid point set generated in the polling process;
if no better solution is found in the searching and polling processes, the method comprises the steps ofUpdate parameter->Reducing the grid size, and searching for a local better solution; if a better solution is generated in the searching and polling processes, updating the current optimal solution, and maintaining or expanding grid size parameters to quickly search the global optimal solution until the grid size reaches a set value, namely stopping searching; when the constraint condition is processed by the MADS algorithm, the minimum circle curve radius and the minimum relaxation curve length are used as insurmountable constraint, in the searching process, whether the grid point meets the insurmountable constraint condition is judged, if not, the grid point is abandoned, and whether the next grid point meets the constraint condition is continuously judged; the allowable adjustment of the critical structure is regarded as surmountable constraint In the searching process, if the grid points do not meet the surmountable constraint condition, adaptively reducing in the iterative process until solutions meeting all control point constraints are searched;
(3) PSO algorithm is adopted and based onAnd->Updating related parameters of the longitudinal line scheme, and ensuring that the parameters meet all constraint conditions; setting a moderation curve, a positive line turnout and a bright bridge deck as a vertical curve forbidden zone, and calculating the minimum vertical curve length according to a formula 15) under the condition that the variable slope point is far enough from the vertical curve forbidden zone to ensure the shortest vertical curve length:
15）；
slope point change mileage when vertical curve length is minimumAnd nearest feature point->Point and->Mileage difference ∈10 between points>Equation 16) should be satisfied:
16）；
in the formula 16), the amino acid sequence of the formula,connecting line corner for adjacent slope changing points>Half of (2);
obtaining the mileage range of the variable slope point according to the formula 16), adopting a speed update formula and a position update formula in the formula 13), and updating the mileage of the variable slope point once by combining constraint conditionsThe method comprises the steps of carrying out a first treatment on the surface of the The position of the slope change point after updating is +.>From equations 15), 16):
17）；
front-rear gradient of slope changing point：
18）；
Solving inequalities 17) and 18) to find the elevation of the slope pointIs used for updating the primary slope change point elevation in the range by combining the constraint condition and the speed update formula and the position update formula of the formula 13) >The method comprises the steps of carrying out a first treatment on the surface of the At this time->And->It is known that the formula is updated according to the speed of inequality 17) and formula 13)And the position update formula updates the vertical curve radius.
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