CN117708961B - 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:
Taking intersection point coordinates of a line plane, front relaxation curve length, rear relaxation curve length, circle curve radius, slope change point mileage of a longitudinal plane and slope change point elevation and vertical curve radius as optimization variables, setting the total number of plane intersection points of the whole line as n and the total number of slope change points as m, and representing three-dimensional space line positions of the line to be optimized by the following vectors:
intersection X coordinate column vector: x= [ X 1,X2,...,Xn]T;
Intersection Y coordinate column vector: y= [ Y 1,Y2,...,Yn]T;
Front relaxation curve length column vector: l F＝[lF1,lF2,...,lFn]T;
Circular curve radius column vector:
Post-relaxation curve length column vector: l B＝[lB1,lB2,...,lBn]T;
Slope change point mileage column vector: l= [ L 1,L2,...,Lm]T;
Slope change point Gao Chenglie vector: z= [ Z 1,Z2,...,Zm]T;
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):
In formula 1):
p T denotes the field measured point set, P T＝{Pi(xi,yi,zi), I e I }, I e i= {1,2, &..k };
m R represents the line column vector of the existing railway three-dimensional space;
d i represents the distance from the measurement point P i to the projection point of the reconstruction line;
f d represents a function of calculating the measurement point adjustment amount;
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 be ax+by+c=0 (ab+.0), the planar adjustment amount of the measurement point P s(xi,yi on the linear element is:
(2) Circular curve line element
Let the fitted round curve equation beThe plane adjustment amount of the measuring point P s(xi,yi on the circular curve line element) is:
In the formula 3), (x H,yH) is the center coordinates of the reconstruction plane circular curve equation, and R H is the radius of the reconstruction plane circular curve;
(3) Moderating curve line element
For the relaxation curve, the planar adjustment amount is calculated iteratively by adopting a dichotomy: setting the included angle between the tangent line at the circular slow point P YH (x, y) and the connecting line of the measuring point P s(xi,yi as alpha YH, setting the included angle between the tangent line at the slow point P HZ (x, y) and the connecting line of the measuring point P s(xi,yi as alpha HZ, selecting the midpoint position P (x ', y') of the slow curve, stopping iteration if the included angle between the tangent line at the point P (x ', y') and the connecting line of the measuring point is equal to pi/2 or smaller than a set threshold value, and obtaining the distance d h i from the point P s(xi,yi) to the point P (x ', y') as the plane adjustment quantity of the measuring point; otherwise, continuing iteration by taking P (x ', y') as the end point of the relaxation curve 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
Assuming that the linear element equation of the reconstruction longitudinal plane is y=kx+b, the lifting and falling path amount (i.e. adjustment amount) of the linear part measuring point P s(xi,yi is:
In the formula 4), K is the slope of a reconstructed longitudinal slope linear equation, namely the reconstructed linear slope, and b is the intercept of the reconstructed longitudinal slope linear equation;
(2) Vertical curve line element
Let the curve equation of the vertical curve beThen the adjustment amount/>, of the measuring point P s(xi,yi) located within the vertical curveThe method comprises the following steps:
in the formula 5), (x V,yV) is the center coordinates of the vertical curve of the reconstructed longitudinal surface; r V is the radius of the vertical curve of the reconstructed longitudinal plane.
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
In formula 6), L cmin is the minimum circular curve length of the plane, D i is the straight line length of the clamp,Is the rotation angle of the slow point P HY (x, y) to the circular slow point P YH (x, y)/>Reconstructing the plane curve radius of the line, wherein l is the length of the moderation curve;
(2) Longitudinal plane restraint
In the formula (7), the amino acid sequence of the formula (I),Is the length of the slope section between adjacent variable slope points, -i Dmax is the maximum allowable descending slope, i Umax is the maximum allowable ascending slope, |Δi i | is the algebraic difference of the slope sections of adjacent slope sections, Δi max is the maximum algebraic difference of the slope sections,/>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:
f(MR,Ps,is,ie)≤dltd 8)；
In the formula 8), f (M R,Ps,is,ie) is a function for calculating the movement amount of the cross section, i s is the gradient of the roadbed, i e is the gradient of the embankment or cutting, and d ltd is the distance from the roadbed to the 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:
Formula 9):
Represents the i-th flat curve starting mileage,/> Represents the i-th flat curve endpoint mileage,/>Represents the i-th vertical curve starting mileage,/>Indicating the ith vertical curve end mileage;
The amount of site adjustment for which there is a limit to the engineering structure should meet the allowable adjustment amount requirement, expressed as:
In formula 10), d minL is the minimum adjustment amount of the measuring point to the left, d maxR is the maximum adjustment amount of the measuring point to the right, d minU is the minimum adjustment amount of the measuring point to the upper, and d maxD is the maximum adjustment amount of the measuring point to the lower.
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;
from the coordinates and mileage of the measurement point P s(xi,yi), the azimuth angle change rate θ i' of the measurement point P s(xi,yi) is obtained, specifically,
In equation 11), θ i is the azimuth of the measurement point P s(xi,yi),Mileage for station P s(xi,yi);
The azimuth angle change rates of the measuring points P 2 and P k-1 are calculated in sequence, the azimuth angle change rate of the 1 st measuring point is 0, and the azimuth angle change rate of the kth measuring point is equal to the azimuth angle change rate of the k-1 th measuring point; let the maximum allowable curve radius of the line be Then 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;
The gradient change rate Q i' of the measuring point P s(xi,yi) is obtained according to the coordinates and mileage of the measuring point P s(xi,yi), specifically,
In formula 12), H i is the elevation of the measuring point P s(xi,yi), and Q' i is the gradient of the measuring point P s(xi,yi);
The gradient change rates of the measuring points P 2 and P k-1 are calculated in sequence, the gradient change rate of the 1 st measuring point is 0, and the gradient change rate of the kth measuring point is equal to the gradient change rate of the k-1 th measuring point; the gradient change rate of the linear 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 the gradient change rate Q i "is considered to be 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;
Formula 13):
V i t is the velocity vector after the ith particle t iteration,
For the position vector after the ith particle t-th iteration,
For the initial position vector of the i-th particle,
P i t is the individual optimal position of the ith particle at the t-th iteration,
P i 0 is the initial optimal position of the ith particle, equal to
Is the global optimum position of the particle swarm,
For a globally optimal position of the initial population of particles,
W is the weight of the inertia, and the weight of the inertia,
C 1、c2 is the acceleration constant of the vehicle,
Random numbers in the range of [0,1 ];
in the MADS algorithm (namely, a grid self-adaptive direct search algorithm), the radius of a plane circle curve and the length of a gentle curve in a variable are searched, an objective function F of a search point is evaluated in a set grid set, and an optimal solution is obtained 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 Pos t i updated by the particle swarm algorithm as initial values, sets initial grid search sizes of the plane circle curve radius and the relaxation curve length respectively, sequentially selects test points on grids, calculates function values of the test points according to an objective function F, compares the function values with the function values of the previous grid points, evaluates whether the search is successful or not according to comparison results, determines whether to execute a polling process according to search results, reduces or enlarges the grid search size according to the search or polling results, continues searching and updating an optimal solution 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, 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/>Calculating the adjustment quantity in the range of each intersection point and the slope change point under the constraint condition by combining the constraint condition, and taking the minimum value of the adjustment quantity as/>, wherein the adjustment quantity is respectivelyAnd/>If control constraint exists in the range of each intersection point and each slope change point, the bandwidth of the plane feasible search domain is/>The longitudinal plane is/>Otherwise, the planar feasible search domain bandwidth is/>The longitudinal plane 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 the fitness of each particle according to a formula 1) to obtain an individual optimal solution P i t of the particle, adopting a formula 13) to iteratively update a speed variable and a position variable, calculating the fitness value of all real measuring points of a line scheme represented by the position variable, and updating the individual optimal solution if the iterative particle fitness is superior to the individual optimal solution P i t; if P i t is better than the global optimal solution Then the global optimal solution is updated to P i t based on the individual optimal positions P i t 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, setting iteration count s=0, and starting the initial point as The objective function F is expressed as:
In the formula 14), P j 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 curve Is 100m, and l F0,lB0 is 10m;
Calculating the function value of each point according to the formula 14) in the grid searching process, if the new grid point F (x s+1)＜F(xs), searching successfully, updating the optimal solution x s, and simultaneously updating the parameter s=s+1 for the next iteration; otherwise, turning to a polling process, estimating an objective function of a point in a neighboring 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 an optimal solution x s, and updating a parameter s=s+1; 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, let x s+1＝xs update the parameter s=s+1, reduce the grid size, and search 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) Based on P i t and by adopting PSO algorithm 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:
when the length of the vertical curve is minimum, the mileage difference delta L between the slope change point mileage L i and the nearest characteristic point ZY point and YZ point should satisfy the formula 16):
in 16), beta is the connecting angle of 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 L i of the variable slope point once by combining constraint conditions; the position of the slope point is changed after updating to be From equations 15), 16):
Slope i i-1、ii before and after the change of slope point:
Solving inequality 17) and 18) to obtain the value range of the elevation Z i of the variable slope point, and updating the elevation Z i of the variable slope point once in the range by combining the constraint condition and the speed update formula and the position update formula of the formula 13); where Δi and Δl are known, the velocity update formula and the position update formula according to inequality 17) and formula 13) update the vertical curve radius.
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 of the line planes, the front relaxation curve length, the rear relaxation curve length, the radius of the circular curve, the slope change point mileage of the longitudinal surface, the slope change point elevation and the vertical curve radius are taken as optimization variables, the total number of plane intersection points of the whole line is set as n, the total number of slope change points is set as m, and the three-dimensional space line position of the line to be optimized is represented by the following vectors:
intersection X coordinate column vector: x= [ X 1,X2,...,Xn]T;
Intersection Y coordinate column vector: y= [ Y 1,Y2,...,Yn]T;
Front relaxation curve length column vector: l F＝[lF1,lF2,...,lFn]T;
Circular curve radius column vector:
Post-relaxation curve length column vector: l B＝[lB1,lB2,...,lBn]T;
Slope change point mileage column vector: l= [ L 1,L2,...,Lm]T;
Slope change point Gao Chenglie vector: z= [ Z 1,Z2,...,Zm]T;
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):
In (a):
p T denotes the field measured point set, P T＝{Pi(xi,yi,zi), I e I }, I e i= {1,2, &..k };
m R represents the line column vector of the existing railway three-dimensional space;
d i represents the distance from the measurement point P i to the projection point of the reconstruction line;
f d represents a function of calculating the measurement point adjustment amount;
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 be ax+by+c=0 (ab+.0), the planar adjustment amount of the measurement point P s(xi,yi on the linear element is:
(2) Circular curve line element
Let the fitted round curve equation beThe plane adjustment amount of the measuring point P s(xi,yi on the circular curve line element) is:
In the formula 3), (x H,yH) is the center coordinates of the reconstruction plane circular curve equation, and R H is the radius of the reconstruction plane circular curve;
(3) Moderating curve line element
For the relaxation curve, the planar adjustment amount is calculated iteratively by adopting a dichotomy: setting the included angle between the tangent line at the circular slow point P YH (x, y) and the connecting line of the measuring point P s(xi,yi as alpha YH, setting the included angle between the tangent line at the slow point P HZ (x, y) and the connecting line of the measuring point P s(xi,yi as alpha HZ, selecting the midpoint position P (x ', y') of the slow curve, stopping iteration if the included angle between the tangent line at the point P (x ', y') and the connecting line of the measuring point is equal to pi/2 or smaller than a set threshold value, and obtaining the distance d h i from the point P s(xi,yi) to the point P (x ', y') as the plane adjustment quantity of the measuring point; otherwise, the iteration is continued with P (x ', y') as the end point of the relaxation curve until the iteration termination condition is satisfied, 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 reconstruction longitudinal plane be y=kx+b, then the lifting and falling channel quantity of the linear part measuring point P s(xi,yi) is:
di v＝|yi-(Kxi+b)| 4)；
In the formula 4), K is the slope of a reconstructed longitudinal slope linear equation, namely the reconstructed linear slope, and b is the intercept of the reconstructed longitudinal slope linear equation;
(2) Vertical curve line element
Let the curve equation of the vertical curve beThen the adjustment amount/>, of the measuring point P s(xi,yi) located within the vertical curveThe method comprises the following steps:
in the formula 5), (x V,yV) is the center coordinates of the vertical curve of the reconstructed longitudinal surface; r V is the radius of the vertical curve of the reconstructed longitudinal plane.
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
In formula 6), L cmin is the minimum circular curve length of the plane, D i is the straight line length of the clamp,Is the rotation angle of the slow point P HY (x, y) to the circular slow point P YH (x, y)/>Reconstructing the plane curve radius of the line, wherein l is the length of the moderation curve;
(2) Longitudinal plane restraint
In the formula (7), the amino acid sequence of the formula (I),Is the length of the slope section between adjacent variable slope points, -i Dmax is the maximum allowable descending slope, i Umax is the maximum allowable ascending slope, |Δi i | is the algebraic difference of the slope sections of adjacent slope sections, Δi max is the maximum algebraic difference of the slope sections,/>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:
f(MR,Ps,is,ie)≤dltd 8)；
In the formula 8), f (M R,Ps,is,ie) is a function for calculating the movement amount of the cross section, i s is the gradient of the roadbed, i e is the gradient of the embankment or cutting, and d ltd is the distance from the roadbed to the 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:
Formula 9):
Represents the i-th flat curve starting mileage,/> Represents the i-th flat curve endpoint mileage,/>Represents the i-th vertical curve starting mileage,/>Indicating the ith vertical curve end mileage;
the amount of site adjustment for which there is a limit to the engineering structure should meet the allowable adjustment amount requirement, expressed as:
/>
In formula 10), d minL is the minimum adjustment amount of the measuring point to the left, d maxR is the maximum adjustment amount of the measuring point to the right, d minU is the minimum adjustment amount of the measuring point to the upper, and d maxD is the maximum adjustment amount of the measuring point to the lower.
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;
from the coordinates and mileage of the measurement point P s(xi,yi), the azimuth angle change rate θ i' of the measurement point P s(xi,yi) is obtained, specifically,
In equation 11), θ i is the azimuth of the measurement point P s(xi,yi),Mileage for station P s(xi,yi);
The azimuth angle change rates of the measuring points P 2 and P k-1 are calculated in sequence, the azimuth angle change rate of the 1 st measuring point is 0, and the azimuth angle change rate of the kth measuring point is equal to the azimuth angle change rate of the k-1 th measuring point; let the maximum allowable curve radius of the line be Then 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 figure 3;
calculating the change rate of the slope of the longitudinal surface, and primarily distinguishing the attribution of the longitudinal surface line elements;
The gradient change rate Q i' of the measuring point P s(xi,yi) is obtained according to the coordinates and mileage of the measuring point P s(xi,yi), specifically,
In formula 12), H i is the elevation of the measuring point P s(xi,yi), and Q' i is the gradient of the measuring point P s(xi,yi);
The gradient change rates of the measuring points P 2 and P k-1 are calculated in sequence, the gradient change rate of the 1 st measuring point is 0, and the gradient change rate of the kth measuring point is equal to the gradient change rate of the k-1 th measuring point; the gradient change rate of the linear 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 the slope change rate Q' i is considered to be 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;
Formula 13):
V i t is the velocity vector after the ith particle t iteration,
For the position vector after the ith particle t-th iteration,
For the initial position vector of the i-th particle,
P i t is the individual optimal position of the ith particle at the t-th iteration,
P i 0 is the initial optimal position for the ith particle, equal to Pos i 0,
Is the global optimum position of the particle swarm,
For a globally optimal position of the initial population of particles,
W is the weight of the inertia, and the weight of the inertia,
C 1、c2 is the acceleration constant of the vehicle,
Random numbers in the range of [0,1 ];
in the MADS algorithm (namely, a grid self-adaptive direct search algorithm), the radius of a plane circle curve and the length of a gentle curve in a variable are searched, an objective function F of a search point is evaluated in a set grid set, and an optimal solution is obtained 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 Pos t i updated by the particle swarm algorithm as initial values, sets initial grid search sizes of the plane circle curve radius and the relaxation curve length respectively, sequentially selects test points on grids, calculates function values of the test points according to an objective function F, compares the function values with the function values of the previous grid points, evaluates whether the search is successful or not according to comparison results, determines whether to execute a polling process according to search results, reduces or enlarges the grid search size according to the search or polling results, continues searching and updating an optimal solution 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/>Calculating the adjustment quantity in the range of each intersection point and the slope change point under the constraint condition by combining the constraint condition, and taking the minimum value of the adjustment quantity as/>, wherein the adjustment quantity is respectivelyAnd/>If control constraint exists in the range of each intersection point and each slope change point, the bandwidth of the plane feasible search domain is/>The longitudinal plane is/>Otherwise, the planar feasible search domain bandwidth isThe longitudinal plane 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 the fitness of each particle according to a formula 1) to obtain an individual optimal solution P i t of the particle, adopting a formula 13) to iteratively update a speed variable and a position variable, calculating the fitness value of all real measuring points of a line scheme represented by the position variable, and updating the individual optimal solution if the iterative particle fitness is superior to the individual optimal solution P i t; if P i t is better than the global optimal solution Then the global optimal solution is updated to P i t based on the individual optimal positions P i t 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, setting iteration count s=0, and starting the initial point as The objective function F is expressed as:
In the formula 14), P j 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 curve Is 100m, and l F0,lB0 is 10m;
Calculating the function value of each point according to the formula 14) in the grid searching process, if the new grid point F (x s+1)＜F(xs), searching successfully, updating the optimal solution x s, and simultaneously updating the parameter s=s+1 for the next iteration; otherwise, turning to a polling process, estimating an objective function of a point in a neighboring 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 an optimal solution x s, and updating a parameter s=s+1; 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, let x s+1＝xs update the parameter s=s+1, reduce the grid size, and search 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) Based on P i t and by adopting PSO algorithm 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:
when the length of the vertical curve is minimum, the mileage difference delta L between the slope change point mileage L i and the nearest characteristic point ZY point and YZ point should satisfy the formula 16):
in 16), beta is the connecting angle of 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 L i of the variable slope point once by combining constraint conditions; the position of the slope point is changed after updating to be From equations 15), 16):
Slope i i-1、ii before and after the change of slope point:
Solving inequality 17) and 18) to obtain the value range of the elevation Z i of the variable slope point, and updating the elevation Z i of the variable slope point once in the range by combining the constraint condition and the speed update formula and the position update formula of the formula 13); where Δi and Δl are known, the velocity update formula and the position update formula according to inequality 17) and formula 13) update the vertical curve radius.
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 P i t and P i t according to a calculation result
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, and the total adjustment quantity of the scheme measuring points optimized by the traditional two-dimensional horizontal and vertical separation type full line oscillation iteration method is 1.22/m 2, and experimental results show that compared with the traditional two-dimensional reconstruction method, the method has the advantages that the total adjustment quantity 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 (9)
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 a three-dimensional line to be reconstructed, a particle swarm algorithm mixed grid self-adaptive direct search algorithm is combined to realize the integral intelligent reconstruction of the line position of the existing railway three-dimensional space;
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, wherein the PSO-MADS hybrid algorithm is a particle swarm algorithm hybrid grid self-adaptive direct search algorithm;
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.
2. The method for integrally intelligently reconstructing the three-dimensional space line bit of the existing railway according to claim 1, wherein the design variables for determining the three-dimensional line to be reconstructed are specifically:
Taking intersection point coordinates of a line plane, front relaxation curve length, rear relaxation curve length, circle curve radius, slope change point mileage of a longitudinal plane and slope change point elevation and vertical curve radius as optimization variables, setting the total number of plane intersection points of the whole line as n and the total number of slope change points as m, and representing three-dimensional space line positions of the line to be optimized by the following vectors:
intersection X coordinate column vector: x= [ X 1,X2,...,Xn]T;
Intersection Y coordinate column vector: y= [ Y 1,Y2,...,Yn]T;
Front relaxation curve length column vector: l F＝[lF1,lF2,...,lFn]T;
Circular curve radius column vector:
Post-relaxation curve length column vector: l B＝[lB1,lB2,...,lBn]T;
Slope change point mileage column vector: l= [ L 1,L2,...,Lm]T;
Slope change point Gao Chenglie vector: z= [ Z 1,Z2,...,Zm]T;
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):
In formula 1):
p T denotes the field measured point set, P T＝{Pi(xi,yi,zi), I e I }, I e i= {1,2, &..k };
m R represents the line column vector of the existing railway three-dimensional space;
d i represents the distance from the measurement point P i to the projection point of the reconstruction line;
f d represents a function of calculating the measurement point adjustment amount;
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 3, 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 be ax+by+c=0, ab not equal to 0, the plane adjustment amount of the measurement point P s(xi,yi) on the linear element is:
(2) Circular curve line element
Let the fitted round curve equation beThe plane adjustment amount of the measuring point P s(xi,yi on the circular curve line element) is:
In the formula 3), (x H,yH) is the center coordinates of the reconstruction plane circular curve equation, and R H is the radius of the reconstruction plane circular curve;
(3) Moderating curve line element
For the relaxation curve, the planar adjustment amount is calculated iteratively by adopting a dichotomy: setting the included angle between the tangent line at the circular slow point P YH (x, y) and the connecting line of the measuring point P s(xi,yi as alpha YH, setting the included angle between the tangent line at the slow point P HZ (x, y) and the connecting line of the measuring point P s(xi,yi as alpha HZ, selecting the midpoint position P (x ', y') of the slow curve, stopping iteration if the included angle between the tangent line at the point P (x ', y') and the connecting line of the measuring point is equal to pi/2 or smaller than a set threshold value, and obtaining the distance d h i from the point P s(xi,yi) to the point P (x ', y') as the plane adjustment quantity of the measuring point; otherwise, continuing iteration by taking P (x ', y') as the end point of the relaxation curve 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 3, wherein the distance from the measuring point to the projection point of the longitudinal plane of the reconstructed line is calculated by the following steps:
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 reconstruction longitudinal plane be y=kx+b, then the lifting and falling channel quantity of the linear part measuring point P s(xi,yi) is:
In the formula 4), K is the slope of a reconstructed longitudinal slope linear equation, namely the reconstructed linear slope, and b is the intercept of the reconstructed longitudinal slope linear equation;
(2) Vertical curve line element
Let the curve equation of the vertical curve beThen the adjustment amount/>, of the measuring point P s(xi,yi) located within the vertical curveThe method comprises the following steps:
in the formula 5), (x V,yV) is the center coordinates of the vertical curve of the reconstructed longitudinal surface; r V is the radius of the vertical curve of the reconstructed longitudinal plane.
6. The method for integrally intelligently reconstructing the three-dimensional space line bit of the existing railway according to claim 2, 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
In formula 6), L cmin is the minimum circular curve length of the plane, D i is the straight line length of the clamp,Is the rotation angle of the slow point P HY (x, y) to the circular slow point P YH (x, y)/>Reconstructing the plane curve radius of the line, wherein l is the length of the moderation curve;
(2) Longitudinal plane restraint
In the formula (7), the amino acid sequence of the formula (I),Is the length of the slope section between adjacent variable slope points, -i Dmax is the maximum allowable descending slope, i Umax is the maximum allowable ascending slope, |Δi i | is the algebraic difference of the slope sections of adjacent slope sections, Δi max is the maximum algebraic difference of the slope sections,/>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:
f(MR,Ps,is,ie)≤dltd 8)；
In the formula 8), f (M R,Ps,is,ie) is a function for calculating the movement amount of the cross section, i s is the gradient of the roadbed, i e is the gradient of the embankment or cutting, and d ltd is the distance from the roadbed to the 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:
Formula 9):
Represents the i-th flat curve starting mileage,/> Represents the i-th flat curve endpoint mileage,/>Represents the i-th vertical curve starting mileage,/>Indicating the ith vertical curve end mileage;
The amount of site adjustment for which there is a limit to the engineering structure should meet the allowable adjustment amount requirement, expressed as:
In formula 10), d minL is the minimum adjustment amount of the measuring point to the left, d maxR is the maximum adjustment amount of the measuring point to the right, d minU is the minimum adjustment amount of the measuring point to the upper, and d maxD is the maximum adjustment amount of the measuring point to the lower.
7. The method for intelligent reconstruction of the three-dimensional space line bit of the existing railway according to claim 3, wherein the obtaining of the initial three-dimensional line scheme is specifically as follows:
calculating azimuth angle change rate of the plane curve measuring point, and primarily distinguishing plane line element attribution;
from the coordinates and mileage of the measurement point P s(xi,yi), the azimuth angle change rate θ i' of the measurement point P s(xi,yi) is obtained, specifically,
In equation 11), θ i is the azimuth of the measurement point P s(xi,yi),Mileage for station P s(xi,yi);
The azimuth angle change rates of the measuring points P 2 and P k-1 are calculated in sequence, the azimuth angle change rate of the 1 st measuring point is 0, and the azimuth angle change rate of the kth measuring point is equal to the azimuth angle change rate of the k-1 th measuring point; let the maximum allowable curve radius of the line be Then consider asThe 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;
The gradient change rate Q i' of the measuring point P s(xi,yi) is obtained according to the coordinates and mileage of the measuring point P s(xi,yi), specifically,
In formula 12), H i is the elevation of the measuring point P s(xi,yi), and Q i' is the gradient of the measuring point P s(xi,yi);
The gradient change rates of the measuring points P 2 and P k-1 are calculated in sequence, the gradient change rate of the 1 st measuring point is 0, and the gradient change rate of the kth measuring point is equal to the gradient change rate of the k-1 th measuring point; the gradient change rate of the linear 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 the gradient change rate Q i "is considered to be 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 intelligently reconstructing the three-dimensional space line bit of the existing railway according to claim 1, 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;
Formula 13):
V i t is the velocity vector after the ith particle t iteration,
For the position vector after the ith particle t-th iteration,
For the initial position vector of the i-th particle,
P i t is the individual optimal position of the ith particle at the t-th iteration,
P i 0 is the initial optimal position of the ith particle, equal to
Is the global optimum position of the particle swarm,
For a globally optimal position of the initial population of particles,
W is the weight of the inertia, and the weight of the inertia,
C 1、c2 is the acceleration constant of the vehicle,
Random numbers in the range of [0,1 ];
In the MADS algorithm, searching the radius of the plane circle curve and the length of the buffer curve in the variable, evaluating the objective function F of the search point in the set grid set, and obtaining the optimal solution by continuously and iteratively searching the descending direction and the step length.
9. The method for intelligent reconstruction of the three-dimensional space line bit of the existing railway according to claim 8, 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 respectively And/>Calculating the adjustment quantity in the range of each intersection point and the slope change point under the constraint condition by combining the constraint condition, and taking the minimum value of the adjustment quantity as/>, wherein the adjustment quantity is respectivelyAnd/>If control constraint exists in the range of each intersection point and each slope change point, the bandwidth of the plane feasible search domain is/>The longitudinal plane is/>Otherwise, the planar feasible search domain bandwidth is/>The longitudinal plane 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 the fitness of each particle according to a formula 1) to obtain an individual optimal solution P i t of the particle, adopting a formula 13) to iteratively update a speed variable and a position variable, calculating the fitness value of all real measuring points of a line scheme represented by the position variable, and updating the individual optimal solution if the iterative particle fitness is superior to the individual optimal solution P i t; if P i t is better than the global optimal solution Then the global optimal solution is updated to P i t based on the individual optimal positions P i t 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 an MADS algorithm, setting the grid point count s=0, and taking an initial point as The objective function is expressed as:
In the formula 14), P j 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 curve Is 100m, and l F0,lB0 is 10m;
Calculating the function value of each point according to the formula 14) in the grid searching process, if the new grid point F (x s+1)＜F(xs), searching successfully, updating the optimal solution x s, and simultaneously updating the parameter s=s+1 for the next iteration; otherwise, turning to a polling process, estimating an objective function of a point in a neighboring 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 an optimal solution x s, and updating a parameter s=s+1; 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, let x s+1＝xs update the parameter s=s+1, reduce the grid size, and search 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) Based on P i t and by adopting PSO algorithm 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:
when the length of the vertical curve is minimum, the mileage difference delta L between the slope change point mileage L i and the nearest characteristic point ZY point and YZ point should satisfy the formula 16):
in 16), beta is the connecting angle of 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 L i of the variable slope point once by combining constraint conditions; the position of the slope point is changed after updating to be From equations 15), 16):
Slope i i-1、ii before and after the change of slope point:
Solving inequality 17) and 18) to obtain the value range of the elevation Z i of the variable slope point, and updating the elevation Z i of the variable slope point once in the range by combining the constraint condition and the speed update formula and the position update formula of the formula 13); where Δi and Δl are known, the velocity update formula and the position update formula according to inequality 17) and formula 13) update the vertical curve radius.
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