CN107153741A - A kind of non-fragment orbit simulation adjustment amount is calculated and fine adjusting method - Google Patents
A kind of non-fragment orbit simulation adjustment amount is calculated and fine adjusting method Download PDFInfo
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Abstract
The present invention proposes that a kind of non-fragment orbit simulation adjustment amount is calculated and fine adjusting method, and using the simulation adjustment amount of the automatic calculating benchmark rail of method of fitting iteration, fit procedure includes：The ride comfort and degree of approximation of simulation curve function and calculating simulation curve are tried to achieve first with fitting of a polynomial theory；Then the relation of the exponent number for the simulation curve function that digital simulation goes out and its ride comfort and degree of approximation, so as to finally determine the exponent number of simulation curve function.Required orbital simulation adjustment amount is exactly distance of the offset at track mileage to the simulation curve tried to achieve.This method optimizes track accurate adjustment scheme, improves accurate adjustment efficiency, is adapted to accurate adjustment and the routine servicing of ballastless track of high-speed railway.
Description
Technical field
The present invention is directed the problem of calculating ballastless track of high-speed railway simulation adjustment amount, is related to a kind of based on multinomial
The orbital simulation adjustment amount automation algorithm and ballastless track fine adjustment method of iteration are fitted, it mainly applies to high speed railway fragments-free
The accurate adjustment and maintenance of track.
Background technology
At present, ballastless track of high-speed railway turns into the primary structure form of China or even whole world railroad track.At a high speed
The features such as special line for passenger trains will adapt to train high speed, high density, high security and good comfort level is it is necessary to requiring high-speed railway
The features such as non-fragment orbit has high ride, high stability, high accuracy, short curing time.In addition, with Beijing-Tianjin, Wu Guang, Beijing-Shanghai
And the laying of the high-speed railway such as Shanghai elder brother, the accurate adjustment quality problems of ballastless track of high-speed railway cause numerous scholars and technology
The attention of personnel.
The calculating of elevation and plane adjustment amount is one of most important link in track accurate adjustment.Currently, engineering is in practice most
Conventional method is to adjust software at random by track geometry status measuring instrument to be adjusted.This method has the disadvantage that:
1) this method needs indirect labor to be adjusted manually by fastener, compares wasting manpower and material resources, and efficiency is extremely low；
2) it is in course of adjustment, different operating personnel are uneven because of its experience and technical merit, finally give
Adjusted Option also can be different, therefore can not obtain a high-quality Adjusted Option.
Therefore, it is necessary to a kind of new algorithm for calculating non-fragment orbit simulation adjustment amount is designed, it is a set of high-quality to obtain
The Adjusted Option of amount.
The content of the invention
Technical problem solved by the invention is in view of the shortcomings of the prior art, to propose a kind of non-fragment orbit simulation adjustment
Amount is calculated and fine adjusting method, and orbital simulation adjustment amount can be calculated automatically.
Technical scheme provided by the present invention is：
A kind of non-fragment orbit simulates adjustment amount computational methods, and the simulation adjustment amount of Calculation Plane benchmark rail includes following step
Suddenly：
Step A1：Read in the design abscissa and actual measurement abscissa at each test point of track；Measured Coordinates are track at this
Mileage is in coordinate value actually measured under earth coordinates；Design coordinate is track at the mileage under earth coordinates
Theoretical value；
Step A2：The difference of the design abscissa and actual measurement abscissa at each test point of track is calculated, each test point is obtained
The track transversal displacement at place；
Step A3：Fitting of a polynomial is carried out to track transversal displacement, simulation curve function is fitted；
Step A4：Bring the mileage of test point into simulation curve function and calculating simulation curvilinear function value；In test point
There is corresponding relation in journey, its mileage can be released by its coordinate with its coordinate；
Step A5：The difference z of calculating simulation curvilinear function value and corresponding track transversal displacement, obtains simulating adjustment amount；
Step A6：Track transversal displacement and simulation adjustment amount sum are calculated first, it is laterally inclined as new track
Shifting amount；Then repeat step A3-A5, until the simulation adjustment amount that step A5 is obtained is 0；By in iterative process, each round step
A5 calculates obtained simulation adjustment amount and is added, and obtains the datum plane rail simulation adjustment amount at this.
In the step A3, comprising the following steps that for simulation curve function is fitted：
a1)：The fitting of a polynomial of different rank is carried out to the transversal displacement of track, the simulation for obtaining different rank is bent
Line；And analyze the smooth degree of the simulation curve of different rank；
a2)：Analyze the smooth degree of the simulation curve of different rank：
First, the first derivative y' and second dervative y " of the simulation curve of different rank are sought；
Then, the radius of curvature of the simulation curve of different rank is sought according to below equation：
Finally, the ride comfort of the simulation curve of different rank is judged according to radius of curvature ρ size, radius of curvature is got over
Greatly, illustrate that flexibility is higher, i.e. the smooth degree of curve is higher；
a3)：The degree of approximation δ of the simulation curve of different rank is evaluated using below equation：
Wherein, P (xi) represent simulation curve functional value, yiRepresent the transversal displacement of track before adjustment；
a4)：Combining step a2) and step a3) result, using be provided simultaneously with high ride and high degree of approximation as principle determine
The exponent number of simulation curve, so as to fit simulation curve function.
In the step A5, simulation adjustment measures the amount of the integral multiple closest to z and for 0.5mm or 1mm.High-speed railway without
During tiny fragments of stone, coal, etc. orbit adjusting, mainly it is adjusted by the rail clip (backing plate etc.) to absolute fix, and China's high speed at present
The dimensions of railway ballastless track gauge apron and back shim is generally all 0.5mm integral multiple and 1mm integral multiple,
Therefore simulation adjustment amount should take 0.5mm or 1mm integral multiple.
A kind of non-fragment orbit simulates adjustment amount computational methods, calculates the simulation adjustment amount of height datum rail and includes following step
Suddenly：
Step B1：Read in the design ordinate and actual measurement ordinate at each test point of track；
Step B2：The difference of the design ordinate and actual measurement ordinate at each test point of track is calculated, each test point is obtained
The track vertical misalignment amount at place；
Step B3：Fitting of a polynomial is carried out to track vertical misalignment amount, simulation curve function is fitted；
Step B4：Bring the mileage of test point into simulation curve function and calculating simulation curvilinear function value；
Step B5：The difference of calculating simulation curvilinear function value and corresponding track vertical misalignment amount, obtains simulating adjustment amount, mould
0.5mm or 1mm integral multiple should be taken by intending adjustment amount；
Step B6：Track vertical misalignment amount and simulation adjustment amount sum are calculated first, it is longitudinally inclined as new track
Shifting amount；Then repeat step B3-B5, until the simulation adjustment amount that step B5 is obtained is 0；By in iterative process, each round step
B5 calculates obtained simulation adjustment amount and is added the height datum rail simulation adjustment amount obtained at this.
In the step B3, comprising the following steps that for simulation curve function is fitted：
b1)：The fitting of a polynomial of different rank is carried out to the transversal displacement of track, the simulation for obtaining different rank is bent
Line；
b2)：Analyze the smooth degree of the simulation curve of different rank；
The smooth degree method of simulation curve of the analysis different rank is：
First, the first derivative y' and second dervative y " of the simulation curve of different rank are sought；
Then, the radius of curvature of the simulation curve of different rank is sought according to below equation：
Finally, the ride comfort of the simulation curve of different rank is judged according to radius of curvature ρ size, radius of curvature is got over
Greatly, illustrate that flexibility is higher, i.e. the smooth degree of curve is higher.
b3)：The degree of approximation δ of the simulation curve of different rank is evaluated using below equation：
Wherein, P (xi) represent simulation curve functional value, yiRepresent the vertical misalignment amount of track before adjustment；
b4)：Combining step b2) and step b3) result, using be provided simultaneously with high ride and high degree of approximation as principle determine
The exponent number of simulation curve, so as to fit simulation curve function.
In the step B5, simulation adjustment measures the amount of the integral multiple closest to z and for 0.5mm or 1mm.
A kind of ballastless track fine adjustment method, calculates the datum plane rail of each position of non-fragment orbit according to the above method first
Simulate adjustment amount and height datum rail simulation adjustment amount；Then, adjustment amount and elevation are simulated according to the datum plane rail calculated
The size of benchmark rail simulation adjustment amount is adjusted to the rail clip and backing plate of non-fragment orbit relevant position.
The principle of the invention is；
The present invention proposes a kind of non-fragment orbit simulation adjustment amount computational methods based on fitting of a polynomial iteration, using plan
The simulation adjustment amount of the automatic calculating benchmark rail of method of iteration is closed, fit procedure includes：Asked first with fitting of a polynomial theory
Obtain the ride comfort and degree of approximation of simulation curve function and calculating simulation curve；Then the simulation curve function that digital simulation goes out
Exponent number and its ride comfort and the relation of degree of approximation, so as to finally determine the exponent number of simulation curve function.Required orbital simulation is adjusted
Whole amount is exactly distance of the offset at track mileage to the simulation curve tried to achieve.
(1) simulation curve function is tried to achieve using fitting of a polynomial theory
It is assumed that data-oriented point (xi,yi) (i=0,1 ..., m), φ is that all number of times are no more than n (n<M) multinomial structure
Into function class, now seek a n functionSo that
When fitting function is multinomial, referred to as fitting of a polynomial meets the P of formula (1)n(x) it is referred to as least square fitting
Multinomial.Especially, as n=1, referred to as linear fit or fitting a straight line.
Obvious δ is a0,a1,...,anThe function of many variables, the necessary condition for seeking extreme value by the function of many variables obtains：
I.e.：
Formula (3) is on a0,a1,...,anSystem of linear equations, be expressed as with the form of matrix：
Formula (4) is a symmetric positive definite matrix, therefore existence and unique solution.Therefore, n can be carried out to the offset of each test point
The fitting of a polynomial of order, fits simulation curve function.
(2) ride comfort of simulation curve
First derivative and second dervative are asked to the simulation curve of different rank, according to curvature radius formula
Wherein：Y' is the first derivative of simulation curve function；Y " is the second dervative of simulation curve function；
Radius of curvature is bigger, illustrates that flexibility is higher, i.e. the smooth degree of curve is higher.The mould of different rank is analyzed with this
The smooth degree of pseudocurve function.
(3) degree of approximation of simulation curve
Simulation curve will not only approach actual track line style, and smooth out as far as possible.Weigh a curve and approach original
The degree of beginning discrete point is represented with formula (5)：
In formula, δ is the degree of approximation of simulation curve；P(xi) it is simulation curve functional value；yiFor the horizontal, vertical of the preceding track of adjustment
To offset.
Bring the horizontal of non-fragment orbit, vertical misalignment amount and simulation curve functional value into formula (5) and formula (6), analysis is different
The simulation curve function of exponent number and orbital forcing and the relation of degree of approximation, the final exponent number for determining simulation curve function.Track
It is distance of the offset at this to simulation curve to simulate adjustment amount, and its size must be 0.5mm or 1mm integral multiple.
Beneficial effect：
The present invention can utilize the automatic Calculation Plane benchmark rail of mode of fitting of a polynomial iteration and the mould of height datum rail
Intend adjustment amount, a set of high-quality tune rail scheme is obtained, to recover the ride comfort of ballastless track of high-speed railway, it is ensured that train is pacified
Row for the national games.This method global optimization orbital simulation adjustment amount computational methods, and save substantial amounts of manpower and materials, improve essence
Efficiency is adjusted, is adapted to accurate adjustment and the regular maintenance of ballastless track of high-speed railway.
Brief description of the drawings
Fig. 1 is the operating process that Calculation Plane benchmark rail simulates adjustment amount；
Fig. 2 is the related procedure for fitting simulation curve.
Embodiment
In order that the purpose of the present invention, technical scheme and advantage are more clearly understood, below in conjunction with drawings and Examples
The present invention is described in further detail.It should be appreciated that specific embodiment described herein is used only for explaining this hair
It is bright, do not limit the present invention.In addition, this example only illustrates that Calculation Plane benchmark rail simulates the related procedure of adjustment amount, height datum
The Computing Principle of the simulation adjustment amount of rail is similar, and here is omitted.
Accompanying drawing 1 is the operating process that Calculation Plane benchmark rail of the present invention simulates adjustment amount, and step is as follows：
Step 1：Read in the Measured Coordinates and design coordinate of track；
Step 2：Calculate the track transversal displacement at each test point；
Step 3：Fitting of a polynomial is carried out to track transversal displacement, simulation curve function is fitted；
Step 4：Bring the mileage of test point into simulation curve function and calculating simulation curvilinear function value；
Step 5：Utilize simulation curve functional value and corresponding track transversal displacement calculating simulation adjustment amount, simulation adjustment
Amount should take 0.5mm or 1mm integral multiple；
Step 6：Track transversal displacement and simulation adjustment amount sum are calculated first, as new track lateral shift
Amount；Then repeat step 2-5, is 0 up to simulating adjustment amount；By in iterative process, what the calculating of each round step 5 was obtained will calculate
The simulation adjustment amount gone out is added the datum plane rail simulation adjustment amount obtained at this.
The present invention carries out track accurate adjustment using the simulation curve function fitted, and accompanying drawing 2 is the phase for fitting simulation curve
Flow is closed, step is as follows：
Step 1：The fitting of a polynomial of different rank is carried out to track transversal displacement, and it is bent to analyze the simulation of different rank
Relation between line and track transversal displacement oscillogram.
Step 2：The simulation curve functional value fitted is utilized into formula
Come the smooth degree of the simulation curve of evaluating different rank, wherein δ represents the degree of approximation of simulation curve, P (xi) represent
Simulation curve functional value, yiRepresent the transversal displacement of track before adjustment.
Step 3：The result of com-parison and analysis step 1 and step 2, determines the exponent number of simulation curve, so that it is bent to fit simulation
Line function.
The inventive method optimizes track accurate adjustment scheme, improves accurate adjustment efficiency, is adapted to the essence of ballastless track of high-speed railway
Adjust and routine servicing.
Claims (7)
1. a kind of non-fragment orbit simulates adjustment amount computational methods, it is characterised in that the simulation adjustment amount bag of Calculation Plane benchmark rail
Include following steps：
Step A1：Read in the design abscissa and actual measurement abscissa at each test point of track；
Step A2：The difference of the design abscissa and actual measurement abscissa at each test point of track is calculated, is obtained at each test point
Track transversal displacement；
Step A3：Fitting of a polynomial is carried out to track transversal displacement, simulation curve function is fitted；
Step A4：Bring the mileage of test point into simulation curve function and calculating simulation curvilinear function value；
Step A5：The difference z of calculating simulation curvilinear function value and corresponding track transversal displacement, obtains simulating adjustment amount；
Step A6：Track transversal displacement and simulation adjustment amount sum are calculated first, as new track transversal displacement；
Then repeat step A3-A5, until the simulation adjustment amount that step A5 is obtained is 0；By in iterative process, each round step 5 is calculated
Obtained simulation adjustment amount is added, and obtains the datum plane rail simulation adjustment amount at this.
2. non-fragment orbit according to claim 1 simulates adjustment amount computational methods, it is characterised in that in the step 3, intend
Close out comprising the following steps that for simulation curve function：
a1)：The fitting of a polynomial of different rank is carried out to the transversal displacement of track, the simulation curve of different rank is obtained；And
Analyze the smooth degree of the simulation curve of different rank；
a2)：Analyze the smooth degree of the simulation curve of different rank：
First, the first derivative y' and second dervative y " of the simulation curve of different rank are sought；
Then, the radius of curvature of the simulation curve of different rank is sought according to below equation：
<mrow>
<mi>&rho;</mi>
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<mrow>
<mo>(</mo>
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</mfrac>
</mrow>
Finally, the ride comfort of the simulation curve of different rank is judged according to radius of curvature ρ size, radius of curvature is bigger, says
Bright flexibility is higher, i.e. the smooth degree of curve is higher；
a3)：The degree of approximation δ of the simulation curve of different rank is evaluated using below equation：
<mrow>
<mi>&delta;</mi>
<mo>=</mo>
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<mo>&lsqb;</mo>
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<mo>(</mo>
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<mi>y</mi>
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</msub>
<mo>&rsqb;</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
Wherein, P (xi) represent simulation curve functional value, yiRepresent the transversal displacement of track before adjustment；
a4)：Combining step a2) and step a3) result, using be provided simultaneously with high ride and high degree of approximation as principle determine simulate
Order of a curve number, so as to fit simulation curve function.
3. non-fragment orbit according to claim 1 simulates adjustment amount computational methods, it is characterised in that in the step A5,
Simulation adjustment measures the amount of the integral multiple closest to z and for 0.5mm or 1mm.
4. a kind of non-fragment orbit simulates adjustment amount computational methods, it is characterised in that calculate the simulation adjustment amount bag of height datum rail
Include following steps：
Step B1：Read in the design ordinate and actual measurement ordinate at each test point of track；
Step B2：The difference of the design ordinate and actual measurement ordinate at each test point of track is calculated, is obtained at each test point
Track vertical misalignment amount；
Step B3：Fitting of a polynomial is carried out to track vertical misalignment amount, simulation curve function is fitted；
Step B4：Bring the mileage of test point into simulation curve function and calculating simulation curvilinear function value；
Step B5：The difference of calculating simulation curvilinear function value and corresponding track vertical misalignment amount, obtains simulating adjustment amount, simulation is adjusted
Whole amount should take 0.5mm or 1mm integral multiple；
Step B6：Track vertical misalignment amount and simulation adjustment amount sum are calculated first, as new track vertical misalignment amount；
Then repeat step B3-B5, until the simulation adjustment amount that step B5 is obtained is 0, by iterative process, each round step B5 is calculated
Obtained simulation adjustment amount is added the height datum rail simulation adjustment amount obtained at this.
5. non-fragment orbit according to claim 4 simulates adjustment amount computational methods, it is characterised in that in the step 3, intend
Close out comprising the following steps that for simulation curve function：
b1)：The fitting of a polynomial of different rank is carried out to the transversal displacement of track, the simulation curve of different rank is obtained；
b2)：Analyze the smooth degree of the simulation curve of different rank；
The smooth degree method of simulation curve of the analysis different rank is：
First, the first derivative y' and second dervative y " of the simulation curve of different rank are sought；
Then, the radius of curvature of the simulation curve of different rank is sought according to below equation：
<mrow>
<mi>&rho;</mi>
<mo>=</mo>
<mfrac>
<msup>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msup>
<mi>y</mi>
<mrow>
<mo>&prime;</mo>
<mn>2</mn>
</mrow>
</msup>
<mo>)</mo>
</mrow>
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
</msup>
<mrow>
<mo>|</mo>
<msup>
<mi>y</mi>
<mrow>
<mo>&prime;</mo>
<mo>&prime;</mo>
</mrow>
</msup>
<mo>|</mo>
</mrow>
</mfrac>
</mrow>
Finally, the ride comfort of the simulation curve of different rank is judged according to radius of curvature ρ size, radius of curvature is bigger, says
Bright flexibility is higher, i.e. the smooth degree of curve is higher；
b3)：The degree of approximation δ of the simulation curve of different rank is evaluated using below equation：
<mrow>
<mi>&delta;</mi>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mi>m</mi>
</munderover>
<msup>
<mrow>
<mo>&lsqb;</mo>
<mi>P</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mo>&rsqb;</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
Wherein, P (xi) represent simulation curve functional value, yiRepresent the vertical misalignment amount of track before adjustment；
b4)：Combining step b2) and step b3) result, using be provided simultaneously with high ride and high degree of approximation as principle determine simulate
Order of a curve number, so as to fit simulation curve function.
6. non-fragment orbit according to claim 4 simulates adjustment amount computational methods, it is characterised in that in the step B5,
Simulation adjustment measures the amount of the integral multiple closest to z and for 0.5mm or 1mm.
7. a kind of ballastless track fine adjustment method, it is characterised in that method according to claims 1 to 3 first is calculated without the tiny fragments of stone, coal, etc.
The datum plane rail simulation adjustment amount of each position of track, method according to claim 4~6 calculate non-fragment orbit each
The height datum rail simulation adjustment amount of position；Then, adjustment amount and height datum rail are simulated according to the datum plane rail calculated
The size of simulation adjustment amount is adjusted to the rail clip and backing plate of non-fragment orbit relevant position.
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| CN111950116A (en) * | 2020-06-23 | 2020-11-17 | 中铁第一勘察设计院集团有限公司 | Automatic simulation adjustment method for ballastless track of high-speed railway |
| CN113373827A (en) * | 2021-08-11 | 2021-09-10 | 北京交通大学 | Ballastless track smoothness control method for bridge pier settlement section |
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| CN102251446A (en) * | 2011-04-19 | 2011-11-23 | 铁道第三勘察设计院集团有限公司 | Accurate track plate adjustment quantity determining method for three-dimensional continuous track system |
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| CN111950116A (en) * | 2020-06-23 | 2020-11-17 | 中铁第一勘察设计院集团有限公司 | Automatic simulation adjustment method for ballastless track of high-speed railway |
| CN113373827A (en) * | 2021-08-11 | 2021-09-10 | 北京交通大学 | Ballastless track smoothness control method for bridge pier settlement section |
| CN113373827B (en) * | 2021-08-11 | 2021-11-09 | 北京交通大学 | Ballastless track smoothness control method for bridge pier settlement section |
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Application publication date: 20170912 |