CN103198229A - Move distance calculation method of existing railway curve - Google Patents

Abstract

The invention discloses a move distance calculation method of an existing railway curve. An improved PSO (particle swarm optimization) method is adopted for optimizing radius and transition length of a design curve, and then movement distance of each measuring point is calculated. In the optimization process, a minimum quadratic sum or minimum absolute value sum of movement distance values delta i of the measuring points serve as an objective function. The move distance calculation method of the existing railway curve is capable of reducing dependence on an initial value and is high in adaptability.

Description

Group space computing method of the existing curve of a kind of railway

Technical field

The present invention relates to the space computing method of dialling of the existing curve of a kind of railway.

Background technology

The existing line curve adjusting always is present in the maintenance and maintenance business of existing railway, and daily maintenance generally adopts rope to execute, and in the operation of circuit medium-capital overhauling, generally adopts method of deflection angle and coordinate method.This method is the existing curve adjusting problem towards the medium-capital overhauling business, and what generally adopt is to have used method of deflection angle and coordinate method for many years, and what they were measured respectively is the drift angle of existing curve and the coordinate of line midline.Wherein the scope of application of involute method has certain limitation, and calculating gained, to dial the error of distance relevant with the size of drift angle, and do not have the tight computing formula of theory, makes error have disguise.With respect to traditional involute method, coordinate method has theoretical tight, measurement calculating achievement precision advantages of higher, but existing automatic algorithms is in the influence of the precision and the spacing that are subjected to the collection point aspect the linear identification.

Need initial linear parameter is identified and obtained to the curvilinear characteristic point before the existing method optimization calculating, responsive to the parameter initial value, different initial values cause different result of calculation, thereby can not get correct result.To dial amount minimum in control traditionally, generally be absolute value sum with 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 conclusions.

In addition, general computing method fail to consider well the requirement at reference mark.The requirement actual according to the scene, the data of the radius of curve, length of transition curve (hereinafter to be referred as slow long) should be integer, and existing method is not all done the integer processing to parameter.

Therefore, be necessary to design a kind of space computing method of dialling of the brand-new existing curve of railway.

Summary of the invention

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

The technical solution of invention is as follows:

The existing curve of a kind of railway dial space computing method, adopt improved PSO method be particle group optimizing method to the gentle progress row optimization of radius of design curve, calculate dialling apart from amount of each measuring point again, may further comprise the steps:

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

Step 2: utilize improved PSO method to upgrade the gentle long data of radius;

Step 3: according to by radius, slow long design curve and the existing measuring point coordinate of determining, calculate each measuring point to the distance of design curve, be the distance amount of dialling of measuring point;

Step 4: calculating target function value;

With dialling apart from the value Δ of each measuring point _iThe quadratic sum minimum or absolute value sum 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 _Max, if equate, forward step 6 to, otherwise forward step 2 to;

Step 6: when iterations equals maximum iteration time Step _MaxThe time, the radius after obtaining to optimize is gentle long, according to determined design curve position, calculates each measuring point and dials apart from amount.

R and l need satisfy following constraint:

l _min≤l≤l _max

R _min≤R≤R _max；

|Δ _k|≤Δ _k，max(k＝1，2，...，m)；

R in the formula _Min, R _MaxAnd l _Min, l _MaxIt is respectively the bound of the gentle long l of radius R.

In the improved PSO method 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; D gets 1 and at 2 o'clock, and corresponding parameters R and l (namely have x respectively _i=(R _i, l _i) ^T);

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

Wherein,

Be the speed of particle i when the n time iteration;

Be the position of particle i when the n time iteration,

Be equally distributed first random number in interval,

Rand wherein ₁ ⁿFor equally distributed random number in [0,1] [is that the probability that each random number occurs is impartial.】

Be equally distributed second random number in interval,

Rand wherein ₂ ⁿBe equally distributed random number in [0,1];

c ₁And c ₂Be aceleration pulse, be positive constant [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 of the historical desired positions correspondence of each particle among each that records time iteration result.The individual extreme value of optimum solution is the parameter in the PSO algorithm]

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

ω is weight coefficient [generally getting 0.7];

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

F (x _F, y _F) put to any one measuring point on the existing line, establish

[first measuring point is on the straight line of curve front for the last measuring point of a F, need not to calculate group distance, later per 20 meters measuring points, need not after curve finishes dialled on the straight line of distance] subpoint on design curve, the J point is the subpoint of F point on design curve, and the length of FJ is that F orders, and to dial the solution procedure that distance: J orders as follows:

(1) crosses J ₁Point is made the tangent line of design curve, and the intersection point of F point on tangent line is G ₁The point;

(2) solve J according to following formula ₁G ₁Length:

$J_1{\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="HDA00003082173300011.png"\; state="\{\{state\}\}">G</figure-callout>}}_1=\frac{(y_{J_1}-y_F)\sin {\mathrm{\&alpha;}}_{G_{1}F}-(x_{J_1}-x_F)\sin {\mathrm{\&alpha;}}_{G_{1}F}}{\sin ({\mathrm{\&alpha;}}_{J_1{G}_1}-{\mathrm{\&alpha;}}_{G_{1}F})};$

Wherein

Be tangent line J ₁G ₁The position angle,

Be G ₁The position angle of F.

(3) establish J ₁The mileage of point is

According to formula

(i=1,2... n-1) are newly put J at design curve ₂, its mileage

For $L_{J_2}={\mathrm{<figure-callout\; id="1"\; label="L\; J"\; filenames="HDA00003082173300011.png"\; state="\{\{state\}\}">L</figure-callout>}}_{J_{}}+J_1{\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="HDA00003082173300011.png"\; state="\{\{state\}\}">G</figure-callout>}}_1;$

(4) according to formula

(i=1,2 ..., n-1), newly put J ₃, J ₄..., J _n, up to satisfying | 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 the measuring point F that asks.

The gentle long initialization of radius:

The gentle long value of the radius of design curve can be very not big with the difference that needs whole positive existing curve.So initialized to the gentle length of radius the time, can be the reference center value with the value of existing line, again the initialization scope be enlarged.For example, the gentle length of the radius of the existing curve of using in the experiment three is respectively 3000 and 100, just can value scope be decided to be 2000～4000 and 0～200 centered by 3000 and 100 so when the gentle length of radius of initialization design curve.It is the initialization of carrying out that random value is eased up and grown radius in giving scope during initialization.

Beneficial effect:

The existing curve of railway of the present invention dial space computing method, be that tradition is dialled that space computing method combines with population (PSO) algorithm and a kind of new curve adjusting method that forms.The integrated particle cluster algorithm fast convergence rate of this method, the ability of finding the solution is strong and to the insensitive strong point of initial value, be target to dial apart from minimum, the nature of nonlinear integral programming problem that is converted into about the linear parameter of design curve (radius is gentle long) apart from calculating will be dialled, dialling apart from calculating of method of deflection angle and coordinate method can be generally be applicable to.This method also can be applicable to have group distance calculating that the reference mark requires.

The present invention adopts the particle cluster algorithm in the intelligence computation method, reduces the susceptibility of parameter initial value, considers by nature of nonlinear integral programming problem, has realized the gentle long integer of curve.This method is analyzed the different target function to the influence of result of calculation by the comparison to the quadratic sum of dialling amount and two kinds of objective function result of calculations of absolute value sum of dialling amount.In addition, this method is coached the constraint condition of distance by include control in model, can satisfy the requirement at reference mark.

This method advantage applies exists:

(1) can make design curve parameter (sweep, slow long) for integer, meet the engineering actual conditions;

R and L contain the random number item, just because of the random value of its generation, have finally obtained optimum solution by algorithm.After obtaining optimum solution, the R corresponding with optimum solution and L value are exactly the value after optimizing, because R, L and be experienced and understanding one to one.

(2) can handle the situation at reference mark;

(3) initial parameter be need not specific (special) requirements;

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

Description of drawings

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

Fig. 2 is that the subpoint of measuring point on design lines calculates synoptic diagram.

Embodiment

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

The existing curve of a kind of railway dial space computing method, adopt improved PSO method be particle group optimizing method to the gentle progress row optimization of radius of design curve, calculate dialling apart from amount of each measuring point again, may further comprise the steps:

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

Step 2: utilize improved PSO method to upgrade the gentle long data of radius;

Step 3: according to by radius, slow long design curve and the existing measuring point coordinate of determining, calculate each measuring point to the distance of design curve, be the distance amount of dialling of measuring point;

Step 4: calculating target function value;

With dialling apart from the value Δ of each measuring point _iThe quadratic sum minimum or absolute value sum 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 _Max, if equate, forward step 6 to, otherwise forward step 2 to;

Step 6: when iterations equals maximum iteration time Step _MaxThe time, the radius after obtaining to optimize is gentle long, according to determined design curve position, calculates each measuring point and dials apart from amount.

R and l need satisfy following constraint:

l _min≤l≤l _max

R _min≤R≤R _max；

|Δ _k|≤Δ _k，max(k＝1，2，...，m)；

R in the formula _Min, R _MaxAnd l _Min, l _MaxIt is respectively the bound of the gentle long l of radius R.

In the improved PSO method 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; D gets 1 and at 2 o'clock, and corresponding parameters R and l (namely have x respectively _i=(R _i, l _i) ^T);

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

Wherein,

Be the speed of particle i when the n time iteration; Be the position of particle i when the n time iteration, Be equally distributed first random number in interval,

Rand wherein ₁ ⁿFor equally distributed random number in [0,1] [is that the probability that each random number occurs is impartial.】

Be equally distributed second random number in interval,

Rand wherein ₂ ⁿBe equally distributed random number in [0,1];

c ₁And c ₂Be aceleration pulse, be positive constant [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 of the historical desired positions correspondence of each particle among each that records time iteration result.The individual extreme value of optimum solution is the parameter in the PSO algorithm]

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

ω is weight coefficient [generally getting 0.7];

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

F (x _F, y _F) put to any one measuring point on the existing line, establish

[first measuring point is on the straight line of curve front for the last measuring point of a F, need not to calculate group distance, later per 20 meters measuring points, need not after curve finishes dialled on the straight line of distance] subpoint on design curve, the J point is the subpoint of F point on design curve, and the length of FJ is that F orders, and to dial the solution procedure that distance: J orders as follows:

(1) crosses J ₁Point is made the tangent line of design curve, and the intersection point of F point on tangent line is G ₁The point;

(2) solve J according to following formula ₁G ₁Length:

$J_1{\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="HDA00003082173300011.png"\; state="\{\{state\}\}">G</figure-callout>}}_1=\frac{(y_{J_1}-y_F)\sin {\mathrm{\&alpha;}}_{G_{1}F}-(x_{J_1}-x_F)\sin {\mathrm{\&alpha;}}_{G_{1}F}}{\sin ({\mathrm{\&alpha;}}_{J_1{G}_1}-{\mathrm{\&alpha;}}_{G_{1}F})};$

Wherein

Be tangent line J ₁G ₁The position angle,

Be G ₁The position angle of F.

(3) establish J ₁The mileage of point is

According to formula

(i=1,2... n-1) are newly put J at design curve ₂, its mileage

For $L_{J_2}={\mathrm{<figure-callout\; id="1"\; label="L\; J"\; filenames="HDA00003082173300011.png"\; state="\{\{state\}\}">L</figure-callout>}}_{J_{}}+J_1{\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="HDA00003082173300011.png"\; state="\{\{state\}\}">G</figure-callout>}}_1;$

(4) according to formula

(i=1,2... n-1), are newly put J ₃, J ₄..., J _n, up to satisfying | 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 the measuring point F that asks.

Embodiment 1:

Respectively the distance value of dialling that two kinds of objective function optimizations solve is analyzed according to experimental data, and then the optimization effect of objective function estimated (calculate respectively with these two objective functions, and the result contrasts, see Table 2-table 4, can select any one in the practical application as objective function).Δ in method of deflection angle _iThe design lines of expression measuring point i and the involute of existing line poor; Δ in coordinate method _iBe expressed as measurement point to the bee-line of design lines, i.e. measuring point and it is in the distance between subpoint on the curve.

In the existing curve adjusting, preceding adjustment curve length, circular curve radius and long three parameters of back adjustment curve of needing only design curve are decided, and design curve is just unique so determines, it is corresponding to group distance value Δ of each measuring point then _iCan obtain.So only these three parameters just can need be optimized group distance value of measuring point as optimizing variable, delay (when slow length did not wait, method was identical) behind preceding slow the equaling of this method hypothesis, only circular curve radius R and two parameters of mitigation length of curve l are optimized.

The whole center of existing line, basic optimization parameters R and l need satisfy following constraint:

s.t.l _min≤l≤l _max

R _min≤R≤R _max (2)

|Δ _k|≤Δ _k，max(k＝1，2，...，m)

R in the formula _Min, R _MaxAnd l _Min, l _MaxBe respectively the gentle long bound of design parameter radius, according to this method algorithm, bigger scope can be set to find globally optimal solution.

In the engineering reality, can have the situation at reference mark on the existing curve, the constraint condition in the formula | Δ _k|≤Δ _{K, max}Show that reference mark k is controlled condition, this is coached apart from the value Δ _kThe maximum that does not allow to surpass this some permission is dialled apart from Δ _{K, max}(being provided with m reference mark).

The optimizing process of PSO method is as follows:

The PSO algorithm is based on a kind of evolutionary computation method of swarm intelligence, and it has inherent parallel ability and speed of convergence faster.In the PSO algorithm, establish particle colony and formed by N particle, in the D dimension space, fly with certain speed, 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).The flying experience of each particle reference oneself and the flying experience of other particles are adjusted flying speed and the direction of oneself, reach 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 _iEach particle is when search, and the history history of oneself is the most better and interior other particles of colony's (or in neighborhood) are the most better as the reference of flying, and the desired positions that whole colony lives through is exactly the current optimum global extremum gbest that finds of whole colony.Each particle is followed above-mentioned two extreme values and is brought in constant renewal in position and the track of oneself, thereby produces new explanation.

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

$v_{\mathrm{id}}^{t+1}={\mathrm{\&omega;v}}_{\mathrm{id}}^t+{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00003082173300011.png"\; state="\{\{state\}\}">c</figure-callout>}}_1\&CenterDot;{\mathrm{rand}}_1^t({\mathrm{pbest}}_{\mathrm{id}}^t-x_{\mathrm{id}}^t)+c_2\&CenterDot;{\mathrm{rand}}_2^t({\mathrm{gbest}}_d^t-x_{\mathrm{id}}^t)---\left(3\right)$

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

In the formula:

x _i=(x _I1, x _I2..., x _ID) ^TThe current location of expression particle i;

v _i=(v _I1, v _I2..., v _ID) ^TThe speed of expression particle i, d=1,2 ..., D, i=1,2 ..., N;

The historical desired positions of expression particle i;

The historical desired positions of expression population;

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

Be particle i current location; (formula x _i=(R _i, l _i) ^TShown x _iBe R _i, l _iA bivector that constitutes.)

Itself is not the present invention for the PSO algorithm, improves but the present invention is based on this.So be not elaborated, and the top substance of having listed this algorithm.

c ₁And c ₂Be aceleration pulse, be called the study factor, be positive constant, generally get 2.0, the study factor has that the oneself sums up and the ability of excellent individual study in the colony, from but particle position near self historical optimum or intragroup historical optimum point, c ₁Regulate particle at the step-length that flies on self desired positions direction, c ₂Regulate particle in the step-length that flies to overall desired positions direction; In the formula: rand ₁And rand ₂Be two between the pseudo random number of [0,1] scope; ω is called weight coefficient, generally gets 0.7; N is the scale of population, generally gets 200, can be according to calculating the suitable scale adjustment; T=1,2 ..., be number of iterations, maximum iteration time generally gets 200, optimizes when reaching maximum iteration time and finishes, and calculates and dials apart from amount.

Relate to the gentle long integer of design curve radius in the step 2 and handle, concrete grammar is as follows:

Longly be integer because the radius of design curve is gentle, if directly adopt the PSO algorithm again result of calculation to be rounded in real number field search optimum solution, then can exist constraint not satisfy or away from the problem of optimum solution.This method is used in carries out Calculation Method in the integer space, problem is considered as nonlinear integer programming, the population rudimentary algorithm is improved to handle the nature of nonlinear integral programming problem of this belt restraining, make the search volume control of population in integer space, thereby avoided unnecessary real number field search.

In the PSO algorithm, because ω, c in (3) formula ₁, c ₂, rand ₁, rand ₂Existence, can make integer variable change real variable into, cause the search still in real number space, carry out.

Under the prerequisite for integer, if in (3) formula of assurance

Be integer, so in (4) formula

Also be integer, handle so only need to carry out integer to (3) formula, just can guarantee that evolutionary search carries out in integer space.

For the ω v in (3) formula _Id ⁿ, carry out round and handle, namely be taken as int (ω v _Id ⁿ+ 0.5).For in (3) formula

Item, wherein rand ₁ ⁿBe equally distributed random number in [0,1], definition ${\mathrm{\&phi;}}_{\mathrm{id}}^n={\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00003082173300011.png"\; state="\{\{state\}\}">c</figure-callout>}}_1{\&CenterDot;{\mathrm{rand}}_1}^n({\mathrm{pbest}}_{\mathrm{id}}^n-x_{\mathrm{id}}^n),$ Then have

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

Be equally distributed random number in interval, definition here

Distributed area be

Interval In integer count into

Individual integer equiprobability distributes, and each is selected assignment and gives

Probability all be $\frac{1}{m_{\mathrm{id}}^n}.$

In like manner, in (3) formula

, we define

Have equally:

Be equally distributed random number in interval, definition here

Distributed area be Interval

In integer count into

Individual integer equiprobability distributes, and each is selected assignment and gives

Probability all be

Particle rapidity after algorithm improves and the more new formula of position are

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

Dial apart from the amount calculating principle as follows:

The amount of dialling is calculated the raw data form that obtains two kinds basically: the drift angle of measuring point and the coordinate of measuring point, their involute method (method of deflection angle) that to distinguish corresponding traditional and the calculating of coordinate method.This method is used data with these two kinds of forms respectively with the population method, has carried out computing method respectively.Its computation process main difference is the calculating of the amount of dialling (dialling distance).

Based on the drift angle data, the data that obtain are drift angles of each measuring point of curve, calculate the involute length of existing curve and each corresponding point of design curve, with 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 existing curve involute long.

And be that the distance of the existing line center line measuring point that will the survey subpoint corresponding with design lines is as group distance based on Coordinate Calculation.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, its principle is as follows:

F (x _F, y _F) put to any one measuring point on the existing line, establish

Be the subpoint of the last measuring point of a F on design curve, the J point for the F point the subpoint on the design curve (FJ is the normal of J point on curve), the length of FJ is the distance of dialling that F orders.The solution procedure that J is ordered is as follows:

(1) crosses J ₁Point is made the tangent line of design curve, and the intersection point of F point on tangent line is G ₁The point;

(2) can solve J according to formula (9) ₁G ₁Length:

$J_1{\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="HDA00003082173300011.png"\; state="\{\{state\}\}">G</figure-callout>}}_1=\frac{(y_{J_1}-y_F)\sin {\mathrm{\&alpha;}}_{G_{1}F}-(x_{J_1}-x_F)\sin {\mathrm{\&alpha;}}_{G_{1}F}}{\sin ({\mathrm{\&alpha;}}_{J_1{G}_1}-{\mathrm{\&alpha;}}_{G_{1}F})}---\left(9\right)$

Wherein Be tangent line J ₁G ₁The position angle, namely y axle positive dirction is docile and obedient clockwise to J from Fig. 2 ₁G ₁Horizontal sextant angle between the line,

Be G ₁The position angle of F.

(3) establish J ₁The mileage of point is

This concept of mileage is key concept in highway and railway, refers to current point apart from the distance of the starting point of appointment, is newly put J according to formula (10) at design curve ₂, its mileage $L_{J_2}$ For $L_{J_2}={\mathrm{<figure-callout\; id="1"\; label="L\; J"\; filenames="HDA00003082173300011.png"\; state="\{\{state\}\}">L</figure-callout>}}_{J_{}}+J_1{\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="HDA00003082173300011.png"\; state="\{\{state\}\}">G</figure-callout>}}_1,$ 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 put J ₃, J ₄..., J _n, up to satisfying 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 finds the solution the method for intersection point and all is suitable on straight-line segment, adjustment curve section and the circular curve segment of design curve, with regard to not needing the position of measuring point is distinguished in solution procedure like this, thereby has been avoided the trouble of staging treating.

Can solve measuring point F according to above-mentioned method _iSubpoint F on design curve _i', in Fig. 2, be the J point, obtain each subpoint F _i' coordinate after, F _iF _i' straight length

Be the distance of asking in the coordinate method of dialling, yet measuring point may be in design lines inboard or the outside, thereby dial apart from positive and negative difference must be arranged.For positive and negative judgement, algorithm adopts the relatively method judgement of position angle size: obtain measuring point F respectively _iIntersection point point F _i' with measuring point F _I+1Line the position angle

And intersection point point F _i' with measuring point F _I+1Intersection point point F ' _I+1Line the position angle If design curve is for turning left the position angle

The 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 the position angle

The time, measuring point F _I+1In the inboard of design curve, dial apart from Δ _I+1Get negative value, on the contrary get on the occasion of.

Dialling apart from method of the existing curve of the described railway of this method, related experiment is specific as follows:

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

Based on dialling apart from calculating of PSO method, by PSO method and method of deflection angle and coordinate method are carried out combination respectively, the result of calculation that makes the two and the calculating of traditional method of deflection angle group compare to verify the correctness of this method apart from the result.

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 existing curve in the document to dial existing curve measuring point data in the reckoner, and the measuring point coordinate data that the data of the coordinate method of PSO get for measuring point drift angle data-switching thus.

The two kinds of methods in back are all dialled distance with measuring point in experiment quadratic sum is objective function, calculates the radius, slow long and dial distance (wherein the method for deflection angle of PSO has also been considered integer and two kinds of situations of non-integer respectively) of design curve.The result of calculation contrast sees Table 1.

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

By the contrast of the result of calculation of last table as can be seen, the gentle long result of radius of the design curve that calculates based on method of deflection angle and the coordinate method of PSO method is consistent with the value that traditional method of deflection angle calculates, and has shown the correctness of the PSO method of this method proposition.

Test the result of calculation contrast of two: two kinds of objective functions

This experiment is to have verified on the basis of PSO method correctness in experiment one, and the coordinate method optimization that it is used for curve adjusting is calculated.Adopting existing sweep in the experiment respectively is the curve real data of 500,1600 and 3,000 three kinds of different radii scopes, adopts aforementioned two kinds of objective functions to dial distance with the radius of this method calculation Design curve, slow length and each measuring point respectively.

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

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

Table 4 design curve result of calculation

By to the optimization result (table 4) of three groups of different radii curves as can be seen, for same existing curve, adopt respectively with the quadratic sum of dialling amount and the absolute value of dialling amount and be objective function, the optimization result who obtains is basic identical, the result dial apart from quadratic sum with dial apart from absolute value and also more approaching, this existing curve negotiating that radius of three groups of different range just has been described can obtain optimum radius with slow long based on the coordinate method of PSO method, and adopts in these two kinds of targets any one can arrive the amount of dialling as optimization aim and calculate purpose.

Experiment three: the algorithm initial value is to result's influence

The gentle long given initial value scope that needs of radius in the PSO method, in order to it is carried out the initialization assignment, the influence of choosing optimizing the result of initial value is bigger in the classic method, and choosing of initial value had relatively high expectations, and initial value need carry out complicated choosing before calculating.This experiment provides the different initial value scopes of the gentle long value of radius, and peep optimization result's otherness is studied choosing optimizing result's influence of PSO method initial value.It below is the experimental result that goes up example (R=3000) data.

The optimization result of the initial value scope of the different sizes of table 5

The gentle long initial value scope of given different radius as can be seen from the above table, the radius of gained design curve is gentle longly all to converge to same optimum solution.Choosing of initial value not have to influence to optimizing the result substantially, and direct given bigger initial value assignment scope in the practical application has avoided classic method to the demanding shortcoming of initial value.This has illustrated that this method can search in bigger initial value scope, algorithm adaptability is stronger.

Experiment four: dial the situation that the reference mark is arranged in the distance calculating

In the practical operation of existing curve adjusting, there is the problem of reference mark constraint, namely the reference mark dials apart from needing restraint in certain scope.Experiment is the data instance of 3000m with above-mentioned radius, and objective function is got and dialled apart from quadratic sum.Respectively design curve is applied some constraint and multi-point constraint in the experiment, choose measuring point when any retrains No. 20, choose during multi-point constraint No. 20 and No. 22 measuring points, given restriction range is respectively | Δ ₂₀|＜0.001, | Δ ₂₂|＜0.005.

Table 6 has the result of calculation at reference mark

By experimental result as can be seen, coordinate method based on PSO method originally, have the situation (satisfied dialling apart from quadratic sum and minimum) of constraint for single reference mark on the curve and a plurality of reference mark, the design curve radius that can solve under the constraint of reference mark is gentle long, and calculates group distance.On this basis, the measuring point of diverse location is retrained experiment, through the great deal of experiment data analysis, draws following conclusion:

(1) if the reference mark near ZH and HZ point, the gentle long radius with existing curve of the design radial that the solves appearance difference of easing up is bigger.Its reason is because the reference mark is constrained, and near group distance of the measuring point that ZH and HZ point are is subjected to the gentle long influence of design curve radius little, but group distance of other measuring points is subjected to and radius reaches slow long the influence greatly.

(2) if the reference mark near QZ point, the gentle long gentle length of the radius difference with existing curve of the design radial that solves is little; When the reference mark was restrained, group distance of other measuring points was also smaller.

Claims (4)

1. The existing curve of railway dial space computing method, it is characterized in that, adopt improved PSO method be particle group optimizing method to the gentle progress row optimization of radius of design curve, calculate dialling apart from amount of each measuring point again, may further comprise the steps:

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

   Step 2: utilize improved PSO method to upgrade the gentle long data of radius;

   Step 3: according to by radius, slow long design curve and the existing measuring point coordinate of determining, calculate each measuring point to the distance of design curve, be the distance amount of dialling of measuring point;

   Step 4: calculating target function value;

   With dialling apart from the value Δ of each measuring point _iThe quadratic sum minimum or absolute value sum minimum as objective function, namely

   

   Or

   

   Step 5: judge whether iterations equals maximum iteration time Step _Max, if equate, forward step 6 to, otherwise forward step 2 to;

   Step 6: when iterations equals maximum iteration time Step _MaxThe time, the radius after obtaining to optimize is gentle long, according to determined design curve position, calculates each measuring point and dials apart from amount.
2. The existing curve of railway according to claim 1 dial space computing method, it is characterized in that R and l need satisfy following constraint:

   l _min≤l≤l _max

   R _min≤R≤R _max；

   |Δ _k|≤Δ _k，max(k＝1，2，...，m)；

   R in the formula _Min, R _MaxAnd l _Min, l _MaxIt is respectively the bound of the gentle long l of radius R.
3. 3. group space computing method of the existing curve of railway according to claim 1 is characterized in that in the improved PSO method of step 2, the more new formula of particle rapidity and position is

   

   

   D=1,2; D gets 1 and at 2 o'clock, respectively corresponding parameters R and l;

   I=1,2 ..., N; N is the scale of population;

   Wherein,

   

   Be the speed of particle i when the n time iteration; Be the position of particle i when the n time iteration,

   

   Be equally distributed first random number in interval,

   

   Rand wherein ₁ ⁿBe equally distributed random number in [0,1];

   

   Be equally distributed second random number in interval,

   

   Rand wherein ₂ ⁿBe equally distributed random number in [0,1];

   c ₁And c ₂Be aceleration pulse, be positive constant;

   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 that finds of whole colony in search procedure;

   ω is weight coefficient.
4. 4. according to the space computing method of dialling of the existing curve of each described railway of claim 1-3, it is characterized in that dialling of any one measuring point apart from computation process is:

   F (x _F, y _F) put to any one measuring point on the existing line, establish

   

   Be the subpoint of the last measuring point of a F on design curve, the J point is the subpoint of F point on design curve, and the length of FJ is that F orders, and to dial the solution procedure that distance: J orders as follows:

   (1) crosses J ₁Point is made the tangent line of design curve, and the intersection point of F point on tangent line is G ₁The point;

   (2) solve J according to following formula ₁G ₁Length:

   Wherein

   

   Be tangent line J ₁G ₁The position angle,

   

   Be G ₁The position angle of F.

   (3) establish J ₁The mileage of point is

   

   According to formula

   

   (i=1 2...n-1) is newly put J at design curve ₂, its mileage

   

   For

   

   (4) according to formula

   

   (i=1,2... n-1), are newly put J ₃, J ₄..., J _n, up to satisfying | 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 the measuring point F that asks.

Images