CN103198229B - A kind of group space computing method of railway available railway curve - Google Patents

Abstract

What the invention discloses a kind of railway available railway curve dials space computing method, and the PSO method of employing improvement and particle group optimizing method are optimized the gentle length of the radius of design curve, then the distance of dialling calculating each measuring point is measured.In optimizing process, dialling apart from value Δ with each measuring point _iquadratic sum minimum or absolute value sum is minimum as objective function, namely or group space computing method of this railway available railway curve can reduce the dependence to initial value, strong adaptability.

Description

A kind of group space computing method of railway available railway curve

Technical field

What the present invention relates to a kind of railway available railway curve dials space computing method.

Background technology

Both in the maintenance that is always present in existing railway of wired curve adjusting and maintenance business, daily maintenance had generally adopted rope to execute, and in the operation of circuit medium-capital overhauling, generally adopted method of deflection angle and coordinate method.This method is the whole direct problem of available railway curve towards medium-capital overhauling business, and what generally adopt is employed method of deflection angle for many years and coordinate method, and what they were measured respectively is the drift angle of available railway curve and the coordinate of line midline.Wherein the scope of application of involute method has a definite limitation, and the error that calculating gained dials distance is relevant with the size of drift angle, and does not have theoretical tight computing formula, makes error have disguise.Relative to traditional involute method, coordinate method has theoretical tight, survey calculation Result Precision advantages of higher, but existing automatic algorithms is subject to the precision of collection point and the impact of spacing in line type identification.

Existing method optimization needs identify curvilinear characteristic point and obtain initial linear parameter before calculating, and more responsive to initial parameter values, different initial value causes different result of calculation, thus can not obtain correct result.Controlling to dial amount traditionally minimum, be generally using the absolute value sum of the quadratic sum of each measuring point amount of dialling or each measuring point amount of dialling as objective function, but which kind of mode is more suitable for actually, not clear and definite conclusion.

In addition, general computing method fail to consider well the requirement at reference mark.According to on-the-spot actual requirement, the radius of curve, the data of length of transition curve (hereinafter referred to as slow length) should be integer, and existing method does not all do integer process to parameter.

Therefore, group space computing method designing a kind of brand-new railway available railway curve is necessary.

Summary of the invention

Technical matters to be solved by this invention is to provide a kind of group space computing method of railway available railway curve, and group space computing method of this railway available railway curve can reduce the dependence to initial value, strong adaptability.

The technical solution of invention is as follows:

A group space computing method for railway available railway curve, the PSO method that employing improves and particle group optimizing method are optimized the gentle length of the radius of design curve, then calculate group distance amount of each measuring point, comprise the following steps:

Step 1: the radius R of initialization design curve, slow long l, population N and maximum iteration time Step _max;

Step 2: utilize the PSO method improved to upgrade radius and to ease up long data;

Step 3: according to the design curve determined by radius, slow length and existing measuring point coordinate, calculate the distance of each measuring point to design curve, what be measuring point dials distance amount;

Step 4: calculating target function value;

Dialling apart from value Δ with each measuring point _iquadratic sum minimum or absolute value sum is minimum as objective function, namely

$\min \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{{\mathrm{\Δ}}_i}^2$ Or $\min \underset{i=1}{\overset{n}{\mathrm{\Σ}}}\left|{\mathrm{\Δ}}_i\right|;$

Step 5: judge whether iterations equals maximum iteration time Step _maxif, equal, forward step 6 to, otherwise forward step 2 to;

Step 6: when iterations equals maximum iteration time Step _maxtime, obtain the radius after optimizing gentle long, according to determined design curve position, calculate each measuring point and dial apart from amount.

Retrain below R and l demand fulfillment:

l _min≤l≤l _max

R _min≤R≤R _max；

|Δ _k|≤Δ _k，max(k＝1，2，...，m)；

R in formula _min, R _maxand l _min, l _maxthat radius R eases up the bound of long l respectively.

In the PSO method of the improvement of step 2, the more new formula of particle rapidity and position is

${x_{\mathrm{id}}}^{n+1}=x_{\mathrm{id}}^n+v_{\mathrm{id}}^{n+1};$

D=1,2; When d gets 1 and 2, corresponding parameter R and l (namely has x respectively _i=(R _i, l _i) ^t);

I=1,2 ..., N; N is the scale [generally getting 200] of population;

Wherein, for the speed of particle i when n-th iteration; for the position of particle i when n-th iteration, for interval interior equally distributed first random number, wherein rand ₁ ⁿfor in [0,1] interior equally distributed random number, [probability that namely each random number occurs is impartial.】

for interval interior equally distributed second random number, wherein rand ₂ ⁿfor equally distributed random number in [0,1];

C ₁and c ₂be aceleration pulse, be normal number [generally getting 2.0];

Pbest is the individual extreme value of each particle optimum solution that particle itself finds in search procedure; [it is in search procedure, the optimum solution that in each the iteration result recorded, each particle history desired positions is corresponding.The individual extreme value of optimum solution is the parameter in PSO algorithm]

Gbest is the current optimum global extremum found of whole colony in search procedure; [it is in each iterative process of search, the optimum solution that particle best in all particles is corresponding.Optimum global extremum is the parameter in PSO algorithm]

ω is weight coefficient [generally getting 0.7];

4. group space computing method of the railway available railway curve according to any one of claim 1-3, is characterized in that, dialling of any one measuring point apart from computation process is:

F (x _f, y _f) point is both wired meaning measuring points of taking up an official post, if for the last measuring point of a F is [on the straight line of the first measuring point before curve, distance is dialled without the need to calculating, every 20 meters of measuring points later, until curve terminate after without the need to dialling on the straight line of distance] subpoint on design curve, J point is the subpoint of F point on design curve, and the length of FJ is group distance of F point: the solution procedure of J point is as follows:

(1) J is crossed ₁point makes the tangent line of design curve, and the intersection point of F point on tangent line is G ₁point;

(2) J is solved according to following formula ₁g ₁length:

$J_1{G}_1=\frac{(y_{J_1}-y_F)\sin {\mathrm{\α}}_{G_{1}F}-(x_{J_1}-x_F)\sin {\mathrm{\α}}_{G_{1}F}}{\sin ({\mathrm{\α}}_{J_1{G}_1}-{\mathrm{\α}}_{G_{1}F})};$

Wherein for tangent line J ₁g ₁position angle, for G ₁the position angle of F.

(3) J is established ₁the mileage of point is according to formula (i=1,2..., n-1) is newly put J on design curve ₂, its mileage for $L_{J_2}=L_{J_1}+J_1{G}_1;$

(4) according to formula (i=1,2 ..., n-1), newly put J ₃, J ₄..., J _n, until meet | J _ng _n| < ε, wherein ε is a small quantity, gets ε=0.001, then J _npoint is the intersection point point J of F point on design curve, and the length of FJ is group distance of required measuring point F.

Radius eases up long initialization:

The radius of design curve eases up long value can not be very large with the difference of the whole positive available railway curve of needs.So with both wired value for reference center value, then can expand initialisation range when pair radius eases up and grows initialized.Such as, the gentle length of radius of the available railway curve used in experiment three is 3000 and 100 respectively, so just can be worth centered by 3000 and 100 when the radius of initialization design curve eases up long and scope is decided to be 2000 ~ 4000 and 0 ~ 200.That random value pair radius eases up and long carries out initialization in given scope during initialization.

Beneficial effect:

Group space computing method of railway available railway curve of the present invention is a kind of new curve adjusting method that conventional Shift Computation space computing method is combined with population (PSO) algorithm and formed.This method integrated particle cluster algorithm fast convergence rate, the ability that solves are strong and to the insensitive strong point of initial value, to dial apart from minimum as target, to dial distance and calculate the nature of nonlinear integral programming problem be converted into about design curve linear parameter (radius is gentle long), the distance of dialling that generally can be applicable to method of deflection angle and coordinate method calculates.The distance of dialling that this method also can be applicable to have reference mark requirement calculates.

The present invention adopts the particle cluster algorithm in intelligent computation method, reduces the susceptibility of initial parameter values, considers by nature of nonlinear integral programming problem, achieves curve and to ease up long integer.This method, by dialling the quadratic sum of amount and comparing of group absolute value sum two kinds of objective function result of calculations measured, analyzes the impact of different target function on result of calculation.In addition, this method, by including the constraint condition controlling to coach distance in a model in, can meet the requirement at reference mark.

This method advantage applies exists:

(1) design curve parameter (sweep, slow length) can be made to be integer, to meet engineering practice;

R and L contains several at random, just because of the random value that it produces, finally obtains optimum solution by algorithm.After obtaining optimum solution, R and the L value corresponding with optimum solution is exactly the value after optimizing, because R, L and be experienced and understanding one to one.

(2) situation at reference mark can be processed;

(3) to initial parameter without the need to particular/special requirement;

Traditional involute method, the isoparametric calculating of radius lacks tight theoretical foundation, and to dial apart from amount be replace dialling amount with the length difference of involute, and size and the corner of computational accuracy and sweep are relevant.

Accompanying drawing explanation

Fig. 1 is the process flow diagram that PSO algorithm calculates R, l;

Fig. 2 is that the subpoint of measuring point in design lines calculates schematic diagram.

Embodiment

Below with reference to the drawings and specific embodiments, the present invention is described in further details:

A group space computing method for railway available railway curve, the PSO method that employing improves and particle group optimizing method are optimized the gentle length of the radius of design curve, then calculate group distance amount of each measuring point, comprise the following steps:

Step 1: the radius R of initialization design curve, slow long l, population N and maximum iteration time Step _max;

Step 2: utilize the PSO method improved to upgrade radius and to ease up long data;

Step 3: according to the design curve determined by radius, slow length and existing measuring point coordinate, calculate the distance of each measuring point to design curve, what be measuring point dials distance amount;

Step 4: calculating target function value;

Dialling apart from value Δ with each measuring point _iquadratic sum minimum or absolute value sum is minimum as objective function, namely

$\min \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{{\mathrm{\&Delta;}}_i}^2$ Or $\min \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left|{\mathrm{\&Delta;}}_i\right|;$

Step 5: judge whether iterations equals maximum iteration time Step _maxif, equal, forward step 6 to, otherwise forward step 2 to;

Step 6: when iterations equals maximum iteration time Step _maxtime, obtain the radius after optimizing gentle long, according to determined design curve position, calculate each measuring point and dial apart from amount.

Retrain below R and l demand fulfillment:

l _min≤l≤l _max

R _min≤R≤R _max；

|Δ _k|≤Δ _k，max(k＝1，2，...，m)；

R in formula _min, R _maxand l _min, l _maxthat radius R eases up the bound of long l respectively.

In the PSO method of the improvement of step 2, the more new formula of particle rapidity and position is

${x_{\mathrm{id}}}^{n+1}=x_{\mathrm{id}}^n+v_{\mathrm{id}}^{n+1};$

D=1,2; When d gets 1 and 2, corresponding parameter R and l (namely has x respectively _i=(R _i, l _i) ^t);

I=1,2 ..., N; N is the scale [generally getting 200] of population;

Wherein, for the speed of particle i when n-th iteration; for the position of particle i when n-th iteration, for interval interior equally distributed first random number, wherein rand ₁ ⁿfor in [0,1] interior equally distributed random number, [probability that namely each random number occurs is impartial.】

for interval interior equally distributed second random number, wherein rand ₂ ⁿfor equally distributed random number in [0,1];

C ₁and c ₂be aceleration pulse, be normal number [generally getting 2.0];

Pbest is the individual extreme value of each particle optimum solution that particle itself finds in search procedure; [it is in search procedure, the optimum solution that in each the iteration result recorded, each particle history desired positions is corresponding.The individual extreme value of optimum solution is the parameter in PSO algorithm]

Gbest is the current optimum global extremum found of whole colony in search procedure; [it is in each iterative process of search, the optimum solution that particle best in all particles is corresponding.Optimum global extremum is the parameter in PSO algorithm]

ω is weight coefficient [generally getting 0.7];

4. group space computing method of the railway available railway curve according to any one of claim 1-3, is characterized in that, dialling of any one measuring point apart from computation process is:

F (x _f, y _f) point is both wired meaning measuring points of taking up an official post, if for the last measuring point of a F is [on the straight line of the first measuring point before curve, distance is dialled without the need to calculating, every 20 meters of measuring points later, until curve terminate after without the need to dialling on the straight line of distance] subpoint on design curve, J point is the subpoint of F point on design curve, and the length of FJ is group distance of F point: the solution procedure of J point is as follows:

(1) J is crossed ₁point makes the tangent line of design curve, and the intersection point of F point on tangent line is G ₁point;

(2) J is solved according to following formula ₁g ₁length:

$J_1{G}_1=\frac{(y_{J_1}-y_F)\sin {\mathrm{\&alpha;}}_{G_{1}F}-(x_{J_1}-x_F)\sin {\mathrm{\&alpha;}}_{G_{1}F}}{\sin ({\mathrm{\&alpha;}}_{J_1{G}_1}-{\mathrm{\&alpha;}}_{G_{1}F})};$

Wherein for tangent line J ₁g ₁position angle, for G ₁the position angle of F.

(3) J is established ₁the mileage of point is according to formula (i=1,2..., n-1) is newly put J on design curve ₂, its mileage for $L_{J_2}=L_{J_1}+J_1{G}_1;$

(4) according to formula (i=1,2..., n-1), is newly put J ₃, J ₄..., J _n, until meet | J _ng _n| < ε, wherein ε is a small quantity, gets ε=0.001, then J _npoint is the intersection point point J of F point on design curve, and the length of FJ is group distance of required measuring point F.

Embodiment 1:

Experimentally data are analyzed the distance value of dialling that two kinds of objective function optimizations solve respectively, and then the effect of optimization of objective function evaluated (calculate respectively with these two objective functions, and result contrasts, in Table 2-table 4, can be selected any one in practical application as objective function).Δ in method of deflection angle _irepresent the design lines of measuring point i and the difference of both wired involute; Δ in coordinate method _ibe expressed as the bee-line of measurement point to design lines, i.e. measuring point and its distance on curve between subpoint.

The whole center of available railway curve, as long as the front adjustment curve length of design curve, circular curve radius and long three parameters of rear adjustment curve are decided, so design curve is just uniquely determined, it corresponds to group distance value Δ of each measuring point then _ican obtain.So only these three parameters just can need be optimized apart from value dialling of measuring point as optimized variable, this method hypothesis front delaying equals rear slow (when slow length does not wait, method is identical), only circular curve radius R and length of transition curve l two parameters are optimized.

Both wired whole center, retrains below basic Optimal Parameters R and l demand fulfillment:

s.t.l _min≤l≤l _max

R _min≤R≤R _max(2)

|Δ _k|≤Δ _k，max(k＝1，2，...，m)

R in formula _min, R _maxand l _min, l _maxbe that design parameter radius eases up long bound respectively, according to this method algorithm, larger scope can be set to find globally optimal solution.

In engineering reality, available railway curve can have the situation at reference mark, the constraint condition in formula | Δ _k|≤Δ _{k, max}show that reference mark k is controlled condition, this is coached apart from value Δ _kdo not allow the maximum group of distance Δ exceeding the permission of this point _{k, max}(being provided with m reference mark).

The optimizing process of PSO method is as follows:

PSO algorithm is a kind of evolutionary computation method based on swarm intelligence, and it has inherent parallel ability and speed of convergence faster.In PSO algorithm, if particle colony is made up of N number of particle, with the flight of certain speed in D dimension space, solution a: x in the corresponding space of particle i _i=(x _i1, x _i2..., x _iD) ^t(dialling in calculating is two dimension, x _i=(R _i, l _i) ^t).Each particle adjusts flying speed and the direction of oneself with reference to the flying experience of oneself and the flying experience of other particles, reaches new position.The desired positions that each particle lives through in search procedure is exactly the individual extreme value pbest of optimum solution that particle itself finds _i.Each particle is when searching for, using the most better reference as flight of history of other particles in the most better for the history of oneself and colony (or in neighborhood), the desired positions that whole colony lives through is exactly the current optimum global extremum gbest found of whole colony.Each particle follows position and the track that above-mentioned two extreme values constantly update oneself, thus produces new explanation.

Position and the speed renewal equation in the n-th generation of particle i d dimension are as follows:

$v_{\mathrm{id}}^{t+1}={\mathrm{\&omega;v}}_{\mathrm{id}}^t+c_1\&CenterDot;{\mathrm{rand}}_1^t({\mathrm{pbest}}_{\mathrm{id}}^t-x_{\mathrm{id}}^t)+c_2\&CenterDot;{\mathrm{rand}}_2^t({\mathrm{gbest}}_d^t-x_{\mathrm{id}}^t)---\left(3\right)$

$x_{\mathrm{id}}^{t+1}=x_{\mathrm{id}}^t+v_{\mathrm{id}}^{t+1}---\left(4\right)$

In formula:

X _i=(x _i1, x _i2..., x _iD) ^trepresent the current location of particle i;

V _i=(v _i1, v _i2..., v _iD) ^trepresent the speed of particle i, d=1,2 ..., D, i=1,2 ..., N;

represent the history desired positions of particle i;

represent the history desired positions of population;

for the speed of particle i when the t time iteration;

for particle i current location; (formula x _i=(R _i, l _i) ^tindicate x _ir _i, l _ithe bivector formed.)

PSO algorithm itself is not the present invention, but the present invention is based on and this has been improvement.Therefore be not described in detail, and list the substance of this algorithm above.

C ₁and c ₂be aceleration pulse, be called Studying factors, be normal number, generally get 2.0, Studying factors has oneself and to sum up and to the ability of excellent individual study in colony, from but the position of particle near self history optimum or intragroup history optimum point, c ₁particle is regulated to fly to the step-length on self desired positions direction, c ₂regulate particle in the step-length flying to overall desired positions direction; In formula: rand ₁and rand ₂two pseudo random numbers between [0,1] scope; ω is called weight coefficient, generally gets 0.7; N is the scale of population, generally gets 200, can according to the adjustment of calculating suitable scale; T=1,2 ..., be the number of times of iteration, maximum iteration time generally gets 200, optimizing and terminating, calculating and dialling apart from amount when reaching maximum iteration time.

Relate to the integer process that design curve radius eases up long in step 2, concrete grammar is as follows:

Radius due to design curve is gentle long is integer, if directly adopt PSO algorithm result of calculation to be rounded in real number field search optimum solution again, then can there is constraint and not to meet or away from the problem of optimum solution.This method is used in the method carrying out in integer space calculating, problem is considered as nonlinear integer programming, population rudimentary algorithm is improved with the nature of nonlinear integral programming problem processing this belt restraining, the search volume of population is controlled in integer space, thus avoids unnecessary real number field search.

In PSO algorithm, due to ω, c in (3) formula ₁, c ₂, rand ₁, rand ₂existence, integer variable can be made to change real variable into, cause search still carry out in real number space.? for under the prerequisite of integer, if in (3) formula of guarantee for integer, so in (4) formula also be integer, so only need to carry out integer process to (3) formula, just can ensure that evolutionary search is carried out in integer space.

For the ω v in (3) formula _id ⁿ, carry out round process, be namely taken as int (ω v _id ⁿ+ 0.5).For in (3) formula , wherein rand ₁ ⁿfor equally distributed random number in [0,1], definition ${\mathrm{\&phi;}}_{\mathrm{id}}^n=c_1{\&CenterDot;{\mathrm{rand}}_1}^n({\mathrm{pbest}}_{\mathrm{id}}^n-x_{\mathrm{id}}^n),$ Then have

${\mathrm{\&phi;}}_{\mathrm{id}}^n\&Element;\left\{\begin{array}{cc}[0,c_1({\mathrm{pbest}}_{\mathrm{id}}^n-x_{\mathrm{id}}^n)]& {\mathrm{pbest}}_{\mathrm{id}}^n{>x}_{\mathrm{id}}^n\\ [c_1({\mathrm{pbest}}_{\mathrm{id}}^n-x_{\mathrm{id}}^n),0]& {\mathrm{pbest}}_{\mathrm{id}}^n{<x}_{\mathrm{id}}^n\end{array}\right.---\left(5\right)$

for interval interior equally distributed random number, define here distributed area be interval in integer count into individual integer equal-probability distribution, each be selected assignment to probability be all $\frac{1}{m_{\mathrm{id}}^n}.$

In like manner, in (3) formula , we define have equally:

for interval interior equally distributed random number, define here distributed area be interval in integer count into individual integer equal-probability distribution, each be selected assignment to probability be all the more new formula of the particle rapidity after algorithm improvement and position is

${x_{\mathrm{id}}}^{n+1}=x_{\mathrm{id}}^n+v_{\mathrm{id}}^{n+1}---\left(8\right)$

Dial the principle calculated apart from gauge as follows:

The raw data form dialling gauge calculation acquisition has two kinds substantially: the drift angle of measuring point and the coordinate of measuring point, and they have distinguished the correspondence calculating of traditional involute method (method of deflection angle) and coordinate method.Particle swarm optimization is applied the data with these two kinds of forms by this method respectively, has carried out computing method respectively.Its computation process main difference is the calculating of amount of dialling (dialling distance).

Based on the data of drift angle, the data obtained are drift angles of each measuring point of curve, calculate the involute length of available railway curve and each corresponding point of design curve, using both involute length differences as dialling distance: Δ _i=E _si-E _ji, wherein measuring point i place design curve involute is long is E _si=f (l, R, x) (x is the mileage at measuring point i place), E _jifor available railway curve involute is long.

And be as dialling distance using the distance of subpoint corresponding with design lines for surveyed both wired center line measuring point based on the calculating of coordinate.Ask the projection intersection point point of each measuring point on design curve, the spacing of this subpoint and measuring point is dialled distance as measuring point, and its principle is as follows:

F (x _f, y _f) point is both wired meaning measuring points of taking up an official post, if for the subpoint of the upper measuring point of a F on design curve, J point is the subpoint of F point on design curve (FJ is the normal of J point on curve), and the length of FJ is group distance of F point.The solution procedure of J point is as follows:

(1) J is crossed ₁point makes the tangent line of design curve, and the intersection point of F point on tangent line is G ₁point;

(2) J can be solved according to formula (9) ₁g ₁length:

$J_1{G}_1=\frac{(y_{J_1}-y_F)\sin {\mathrm{\&alpha;}}_{G_{1}F}-(x_{J_1}-x_F)\sin {\mathrm{\&alpha;}}_{G_{1}F}}{\sin ({\mathrm{\&alpha;}}_{J_1{G}_1}-{\mathrm{\&alpha;}}_{G_{1}F})}---\left(9\right)$

Wherein for tangent line J ₁g ₁position angle, namely from Fig. 2 y-axis positive dirction according to clockwise direction to J ₁g ₁horizontal sextant angle between line, for G ₁the position angle of F.

(3) J is established ₁the mileage of point is this concept of mileage is a most key concept in highway and railway, refers to the distance of the starting point that current point distance is specified, is newly put J according to formula (10) on design curve ₂, its mileage $L_{J_2}$ For $L_{J_2}=L_{J_1}+J_1{G}_1,$ General formula is

$L_{J_{i+1}}=L_{J_i}+J_i{G}_i$ (I＝1，2...，n-1)(10)

(4) according to formula (10), newly J is put ₃, J ₄..., J _n, until meet formula (11), wherein ε is a small quantity, gets ε=0.001, then J _npoint is the intersection point point J of F point on design curve.

|J _nG _n|＜ε(11)

This solves on the straight-line segment of method at design curve of intersection point, mild wet air oxidation and circular curve segment all applicable, distinguishes like this, thus avoid the trouble of staging treating in solution procedure with regard to not needing to the position of measuring point.

Measuring point F can be solved according to above-mentioned method _isubpoint F on design curve _i', be J point in fig. 2, obtain each subpoint F _i' coordinate after, F _if _i' straight length to be in coordinate method and required to dial distance, but measuring point inside design lines or outside, thus may be dialled apart from there being positive and negative difference.For positive and negative judgement, algorithm adopts the method comparing position angle size to judge: obtain measuring point F respectively _iintersection point point F _i' with measuring point F _i+1line position angle and intersection point point F _i' with measuring point F _i+1intersection point point F ' _i+1line position angle if design curve is for turning left, position angle time, measuring point F _i+1in the outside of design curve, dial apart from Δ _i+1get on the occasion of, otherwise get negative value.If design curve is for turning right, position angle time, measuring point F _i+1in the inner side of design curve, dial apart from Δ _i+1get negative value, on the contrary get on the occasion of.

Group distance method of the railway available railway curve described in this method, involved experiment is specific as follows:

Experiment one: based on the verification of correctness of PSO method

Dial apart from calculating based on PSO method, by PSO method and method of deflection angle and coordinate method being combined respectively, group distance result that the result of calculation of the two and traditional method of deflection angle are calculated carries out contrasting to verify the correctness of the method.

Document (railway construction., Yi Sirong compiles, China Railway Press, 2009) be the result of calculation of traditional method of deflection angle.The method of deflection angle data of PSO directly adopt available railway curve in the document to dial the available railway curve measuring point data in reckoner, and the data of the coordinate method of PSO are the measuring point coordinate data that obtains of measuring point drift angle data conversion thus.

Latter two method all dials the quadratic sum of distance for objective function with measuring point in an experiment, calculates the radius of design curve, slow long and group distance (wherein the method for deflection angle of PSO also considers integer and non-integer two kinds of situations respectively).Result of calculation contrast is in table 1.

The result of calculation of table 1 classic method and PSO method contrasts

Contrasted as can be seen from the result of calculation of upper table, the radius of the design curve that method of deflection angle and coordinate method based on PSO method calculate long result of easing up is consistent with the value that traditional method of deflection angle calculates, and indicates the correctness of the PSO method that this method proposes.

The result of calculation contrast of experiment two: two kinds of objective functions

This experiment is on the basis that experiment one demonstrates PSO method correctness, it is used in the coordinate method optimization calculating of curve adjusting.Adopt available railway curve radius to be the curve real data of 500,1600 and 3,000 three kinds of different radii scopes in experiment respectively, adopt aforementioned two kinds of objective functions respectively with this method calculate the radius of design curve, slow long and each measuring point dials distance.

Dialling apart from result under curve two kinds of objective functions of table 2R=500

Dialling apart from result under curve two kinds of objective functions of table 3R=1600 and R=3000

Table 4 design curve result of calculation

By finding out the optimum results (table 4) of three groups of different radii curves, for same available railway curve, adopt respectively with dial amount quadratic sum with dial measure absolute value and for objective function, the optimum results obtained is substantially identical, result dial apart from quadratic sum with dial apart from absolute value and also relatively, the available railway curve that this illustrates the radius of three groups of different range is by obtaining optimum radius with slow long based on the coordinate method of PSO method, and any one adopting in these two kinds of targets can arrive as optimization aim and dial gauge and calculate object.

Experiment three: algorithm initial value is on the impact of result

The given scope of initial values of the gentle long needs of radius in PSO method, to carry out initialization assignment to it, in classic method initial value choose the impact of optimum results larger, to initial value to choose requirement higher, before calculating, initial value needs to carry out complicated choosing.This experiment provides radius and to ease up the different scope of initial values of long value, the otherness of peep optimization result, the impact chosen optimum results of research PSO method initial value.It is below the experimental result of upper example (R=3000) data.

The optimum results of the scope of initial values of the different size of table 5

Given different radius eases up initial value scope long as can be seen from the above table, and the radius of gained design curve is gentle longly all can converge to same optimum solution.Choosing of initial value does not affect substantially on optimum results, can direct given larger initial value assignment scope in practical application, avoids the shortcoming that classic method is high to initial value requirement.Which illustrate this method to search in larger scope of initial values, algorithm adaptability is stronger.

Experiment four: dial the situation having reference mark in calculating

In the whole positive practical operation of available railway curve, there is the problem of reference mark constraint, namely the distance of dialling at reference mark needs restraint in certain scope.The data instance that experiment is 3000m with above-mentioned radius, objective function is got and is dialled apart from quadratic sum.Respectively to design curve applying some constraint and multi-point constraint in experiment, a bit choose No. 20 measuring points during constraint, choose No. 20 and No. 22 measuring points during multi-point constraint, given restriction range is respectively | Δ ₂₀| < 0.001, | Δ ₂₂| < 0.005.

Table 6 has the result of calculation at reference mark

As can be seen from experimental result, based on the coordinate method of this PSO method, for reference mark single on curve and the constrained situation of multiple reference mark tool (meet and dial apart from quadratic sum and minimum), the design curve radius that can solve under the constraint of reference mark is gentle long, and calculates and dial distance.On this basis, constraint experiment is carried out to the measuring point of diverse location, through a large amount of analysis of experimental data, draws following conclusion:

(1) if reference mark is near ZH and HZ point, the design radial solved long appearance difference of easing up with the radius of available railway curve of easing up is larger.Its reason is because reference mark is constrained, dialling apart from little by the long impact of easing up of design curve radius of the measuring point near ZH and HZ point, but dialling of other measuring points affects greatly apart from by with radius and slow length.

(2) if reference mark is near QZ point, the design radial solved long long difference of easing up with the radius of available railway curve of easing up is little; While reference mark is restrained, dialling apart from also smaller of other measuring points.

Claims (1)

1. a group space computing method for railway available railway curve, is characterized in that, the PSO method that employing improves and particle group optimizing method are optimized the gentle length of the radius of design curve, then calculates group distance amount of each measuring point, comprises the following steps:

Step 1: the radius R of initialization design curve, slow long l, population N and maximum iteration time Step _max;

Step 2: utilize the PSO method improved to upgrade radius and to ease up long data;

Step 3: according to the design curve determined by radius, slow length and existing measuring point coordinate, calculate the distance of each measuring point to design curve, what be measuring point dials distance amount;

Step 4: calculating target function value;

Dialling apart from value Δ with each measuring point _iquadratic sum minimum or absolute value sum is minimum as objective function, namely

or k is measuring point sum;

Step 5: judge whether iterations equals maximum iteration time Step _maxif, equal, forward step 6 to, otherwise forward step 2 to;

Step 6: when iterations equals maximum iteration time Step _maxtime, obtain the radius after optimizing gentle long, according to determined design curve position, calculate each measuring point and dial apart from amount;

Retrain below R and l demand fulfillment:

l _min≤l≤l _max

R _min≤R≤R _max；

| Δ _k|≤Δ _{k, max}k=1,2 ..., m; Wherein Δ _kfor the distance of dialling of reference mark k is worth, Δ _{k, max}for the maximum group of distance that this reference mark k allows, m is reference mark number;

R in formula _min, R _maxand l _min, l _maxthat radius R eases up the bound of long l respectively;

In the PSO method of the improvement of step 2, the more new formula of particle rapidity and position is

${x_{id}}^{n+1}=x_{id}^n+v_{id}^{n+1};$

D=1,2; When d gets 1 and 2, corresponding parameter R and l respectively;

i＝1,2,...,N；

Wherein, for the speed of particle i when n-th iteration; for the position of particle i when n-th iteration;

for interval interior equally distributed first random number, wherein rand ₁ ⁿfor equally distributed random number in [0,1];

for interval interior equally distributed second random number, wherein rand ₂ ⁿfor equally distributed random number in [0,1];

C ₁and c ₂being aceleration pulse, is normal number;

Pbest is the individual extreme value of each particle optimum solution that particle itself finds in search procedure;

Gbest is the current optimum global extremum found of whole colony in search procedure;

ω is weight coefficient;

Dialling of any one measuring point apart from computation process is:

F (x _f, y _f) point is both wired meaning measuring points of taking up an official post, if for the subpoint of the last measuring point of a F on design curve, J point is the subpoint of F point on design curve, and the length of FJ is group distance of F point: the solution procedure of J point is as follows:

(1) J is crossed ₁point makes the tangent line of design curve, and the intersection point of F point on tangent line is G ₁point;

(2) J is solved according to following formula ₁g ₁length:

$J_1{G}_1=\frac{(y_{J_1}-y_F){\mathrm{sin\&alpha;}}_{G_{1}F}-(x_{J_1}-x_F){\mathrm{sin\&alpha;}}_{G_{1}F}}{sin({\mathrm{\&alpha;}}_{J_1{G}_1}-{\mathrm{\&alpha;}}_{G_{1}F})};$

Wherein for tangent line J ₁g ₁position angle, for G ₁the position angle of F;

(3) J is established ₁the mileage of point is according to formula i=1,2..., K-1 are newly put J on design curve ₂, its mileage for

(4) according to formula i=1,2..., K-1, newly put J ₃, J ₄..., J _k, until meet | J _ng _n| < ε, wherein ε is a small quantity, gets ε=0.001, then J _kpoint is the intersection point point J of F point on design curve, and the length of FJ is group distance of required measuring point F.