CN107153741A - A kind of non-fragment orbit simulation adjustment amount is calculated and fine adjusting method - Google Patents

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

Calculation and fine adjustment method of ballastless track simulation adjustment amount

technical field

The present invention is aimed at the problem of calculating the simulation adjustment amount of ballastless track of high-speed railway, and relates to an automatic algorithm of track simulation adjustment amount based on polynomial fitting iteration and a fine adjustment method of ballastless track, which is mainly applied to the ballastless track of high-speed railway Fine tuning and maintenance.

Background technique

At present, high-speed railway ballastless track has become the main structural form of railway tracks in my country and even in the world. In order to adapt to the characteristics of high speed, high density, high safety and good comfort of trains, the high-speed railway passenger dedicated line requires high-speed railway ballastless track to have the characteristics of high ride comfort, high stability, high precision and short maintenance time. In addition, with the laying of Beijing-Tianjin, Wuhan-Guangzhou, Beijing-Shanghai and Shanghai-Kunming high-speed railways, the fine-tuning quality of high-speed railway ballastless tracks has attracted the attention of many scholars and technicians.

The calculation of elevation and plane adjustment is one of the most important links in track fine-tuning. At present, the most commonly used method in engineering practice is to adjust through the random adjustment software of the track geometric state measuring instrument. This method has the following disadvantages:

1) This method needs to be adjusted manually by fasteners manually, which is a waste of manpower and material resources, and the efficiency is extremely low;

2) During the adjustment process, due to the uneven experience and technical level of different operators, the final adjustment plan will be different, so a high-quality adjustment plan cannot be obtained.

Therefore, it is necessary to design a new algorithm for calculating the simulation adjustment of ballastless track to obtain a set of high-quality adjustment schemes.

Contents of the invention

The technical problem solved by the present invention is to propose a method for calculating and fine-tuning the simulated adjustment amount of the ballastless track, which can automatically calculate the simulated adjustment amount of the track.

The technical scheme provided by the present invention is:

A method for calculating a simulated adjustment amount of a ballastless track, the calculation of the simulated adjustment amount of a plane reference rail includes the following steps:

Step A1: Read in the design abscissa and measured abscissa at each detection point of the track; the measured coordinate is the coordinate value actually measured by the track at the mileage in the geodetic coordinate system; the design coordinate is the geodetic coordinate of the track at the mileage The theoretical value under the system;

Step A2: Calculate the difference between the designed abscissa and the measured abscissa at each detection point of the track to obtain the lateral offset of the track at each detection point;

Step A3: Carry out polynomial fitting to the lateral offset of the track, and fit the simulation curve function;

Step A4: Bring the mileage of the detection point into the simulation curve function and calculate the value of the simulation curve function; there is a corresponding relationship between the mileage of the detection point and its coordinates, and its mileage can be deduced from its coordinates;

Step A5: Calculate the difference z between the simulated curve function value and the corresponding track lateral offset to obtain the simulated adjustment amount;

Step A6: First calculate the sum of the orbital lateral offset and the simulated adjustment, and use it as the new orbital lateral offset; then repeat steps A3-A5 until the simulated adjustment obtained in step A5 is 0; , the simulated adjustments calculated in step A5 in each round are added together to obtain the simulated adjustments of the plane reference rail at this place.

In the step A3, the specific steps of fitting the simulation curve function are as follows:

a1): Carry out polynomial fitting of different orders to the lateral offset of the track to obtain simulated curves of different orders; and analyze the smoothness of the simulated curves of different orders;

a2): Analyze the smoothness of simulation curves of different orders:

First, calculate the first-order derivative y' and the second-order derivative y" of the simulation curves of different orders;

Then, calculate the radius of curvature of the simulated curves of different orders according to the following formula:

Finally, the smoothness of the simulated curves of different orders is judged according to the size of the curvature radius ρ. The larger the curvature radius, the higher the curvature, that is, the higher the smoothness of the curve;

a3): Use the following formula to evaluate the approximation δ of the simulation curves of different orders:

Wherein, P( _xi ) represents the function value of the simulation curve, and y _represents the lateral offset of the track before adjustment;

a4): Combining the results of step a2) and step a3), the order of the simulation curve is determined based on the principle of high smoothness and high approximation, so as to fit the simulation curve function.

In the step A5, the analog adjustment amount is the closest to z and is an integer multiple of 0.5 mm or 1 mm. When adjusting the ballastless track of high-speed railway, it is mainly to adjust the track fasteners (backing plate, etc.) Integer multiples of 0.5mm and 1mm, so the analog adjustment should be an integral multiple of 0.5mm or 1mm.

A method for calculating the simulated adjustment amount of a ballastless track, the calculation of the simulated adjustment amount of the elevation reference rail comprises the following steps:

Step B1: read in the design ordinate and measured ordinate at each detection point of the track;

Step B2: Calculate the difference between the design ordinate and the measured ordinate at each detection point of the track to obtain the longitudinal offset of the track at each detection point;

Step B3: Carry out polynomial fitting to the longitudinal offset of the track, and fit the simulation curve function;

Step B4: Bring the mileage of the detection point into the simulation curve function and calculate the value of the simulation curve function;

Step B5: Calculate the difference between the simulated curve function value and the corresponding track longitudinal offset to obtain the simulated adjustment amount, which should be an integer multiple of 0.5mm or 1mm;

Step B6: first calculate the sum of the track longitudinal offset and the simulated adjustment, and use it as the new track longitudinal offset; then repeat steps B3-B5 until the simulated adjustment obtained in step B5 is 0; , the simulated adjustments calculated in step B5 in each round are added to obtain the simulated adjustments of the elevation reference rail at this place.

In the step B3, the specific steps of fitting the simulation curve function are as follows:

b1): Carry out polynomial fitting of different orders to the lateral offset of the track, and obtain simulation curves of different orders;

b2): Analyze the smoothness of the simulation curves of different orders;

The method for smoothness of the simulated curves of different orders of analysis is:

First, calculate the first-order derivative y' and the second-order derivative y" of the simulation curves of different orders;

Then, calculate the radius of curvature of the simulated curves of different orders according to the following formula:

Finally, the smoothness of the simulated curves of different orders is judged according to the size of the radius of curvature ρ. The larger the radius of curvature, the higher the degree of curvature, that is, the higher the smoothness of the curve.

b3): Use the following formula to evaluate the approximation degree δ of the simulation curves of different orders:

Wherein, P( _xi ) represents the function value of the simulation curve, and y _represents the longitudinal offset of the track before adjustment;

b4): Combining the results of step b2) and step b3), the order of the simulation curve is determined based on the principle of high smoothness and high approximation, so as to fit the simulation curve function.

In the step B5, the analog adjustment amount is the closest to z and is an integer multiple of 0.5 mm or 1 mm.

A fine adjustment method for ballastless track, first calculate the simulated adjustment amount of the plane reference rail and the simulated adjustment amount of the elevation reference rail at each position of the ballastless track according to the above method; then, according to the calculated adjustment amount of the plane reference rail simulation and the elevation reference rail The size of the simulated adjustment is adjusted to the track fasteners and backing plates at the corresponding positions of the ballastless track.

Principle of the present invention is;

The present invention proposes a method for calculating the simulation adjustment amount of ballastless track based on polynomial fitting iteration, and adopts the method of fitting iteration to automatically calculate the simulation adjustment amount of the reference rail. Curve function and calculate the smoothness and approximation of the simulated curve; then calculate the relationship between the order of the fitted simulated curve function and its smoothness and approximation, so as to finally determine the order of the simulated curve function. The required track simulation adjustment is the distance from the offset at a certain mileage of the track to the obtained simulation curve.

(1) Using polynomial fitting theory to obtain the simulation curve function

Assume given data points ( _xi , y _i ) (i=0,1,...,m), φ is a function class composed of all polynomials whose degree does not exceed n (n<m), now find an n degree function make

When the fitting function is polynomial, it is called polynomial fitting, and P _n (x) satisfying formula (1) is called least squares fitting polynomial. In particular, when n=1, it is called linear fitting or straight line fitting.

Apparently, δ is a multivariate function of a ₀ , a ₁ ,..., a _n , from the necessary conditions for calculating the extremum of the multivariate function:

which is:

Equation (3) is a system of linear equations about a ₀ , a ₁ ,...,a _n , expressed in matrix form as:

Formula (4) is a symmetric positive definite matrix, so there is a unique solution. Therefore, an n-order polynomial fitting can be performed on the offset of each detection point to fit an analog curve function.

(2) Smoothness of the simulation curve

Calculate the first and second derivatives of simulated curves of different orders, according to the formula of radius of curvature

Among them: y' is the first derivative of the simulated curve function; y" is the second derivative of the simulated curve function;

The larger the radius of curvature, the higher the curvature, that is, the higher the smoothness of the curve. This is used to analyze the smoothness of the simulated curve functions of different orders.

(3) Approximation of the simulation curve

The simulated curve should not only approach the actual track shape, but also be as smooth as possible. The degree to which a curve approaches the original discrete point is expressed by formula (5):

In the formula, δ is the approximation degree of the simulation curve; P( _xi ) is the function value of the simulation curve; y _i is the horizontal and vertical offset of the track before adjustment.

Bring the horizontal and vertical offsets of the ballastless track and the simulated curve function values into formulas (5) and (6), analyze the relationship between the simulated curve functions of different orders and the smoothness and approximation of the track, and finally determine the simulated curve The order of the function. The track simulation adjustment amount is the distance from the offset here to the simulation curve, and its size must be an integer multiple of 0.5mm or 1mm.

Beneficial effect:

The present invention can automatically calculate the simulated adjustment amount of the plane reference rail and the elevation reference rail by means of polynomial fitting iteration, obtain a set of high-quality rail adjustment schemes, restore the smoothness of the ballastless track of the high-speed railway, and ensure the safe operation of the train . This method optimizes the calculation method of track simulation adjustment as a whole, saves a lot of manpower and material resources, improves the fine adjustment efficiency, and is suitable for fine adjustment and daily maintenance of high-speed railway ballastless track.

Description of drawings

Fig. 1 is the operation process of calculating the simulated adjustment amount of the plane reference rail;

Fig. 2 is the relevant process of fitting out the simulation curve.

detailed description

In order to make the purpose, technical solution and advantages of the present invention more clear, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention. In addition, this example only illustrates the related process of calculating the simulated adjustment amount of the plane reference rail. The calculation principle of the simulated adjustment amount of the elevation reference rail is similar, and will not be repeated here.

Accompanying drawing 1 is the operation process of the present invention's calculation plane reference rail simulation adjustment amount, and the steps are as follows:

Step 1: read in the measured coordinates and design coordinates of the track;

Step 2: Calculate the track lateral offset at each detection point;

Step 3: Carry out polynomial fitting to the lateral offset of the track, and fit the simulation curve function;

Step 4: Bring the mileage of the detection point into the simulation curve function and calculate the simulation curve function value;

Step 5: Use the simulated curve function value and the corresponding track lateral offset to calculate the simulated adjustment amount, and the simulated adjustment amount should be an integer multiple of 0.5mm or 1mm;

Step 6: First calculate the sum of the track lateral offset and the simulated adjustment, and use it as the new track lateral offset; then repeat steps 2-5 until the simulated adjustment is 0; during the iterative process, each round Add the calculated simulation adjustments calculated in step 5 to obtain the simulation adjustment of the plane reference rail at this place.

The present invention utilizes the simulated curve function fitted to fine-tune the track. Accompanying drawing 2 is a related process of fitting the simulated curve, and the steps are as follows:

Step 1: Carry out polynomial fitting of different orders to the track lateral offset, and analyze the relationship between the simulated curves of different orders and the waveform diagram of the track lateral offset.

Step 2: Apply the fitted simulation curve function value to the formula

To evaluate the smoothness of the simulation curves of different orders, where δ represents the approximation degree of the simulation curve, P( _xi ) represents the function value of the simulation curve, and y _i represents the lateral offset of the track before adjustment.

Step 3: Analyze and compare the results of Step 1 and Step 2, determine the order of the simulation curve, and then fit the simulation curve function.

The method of the invention optimizes the fine adjustment scheme of the track, improves the fine adjustment efficiency, and is suitable for the fine adjustment and daily maintenance of the ballastless track of the high-speed railway.

Claims (7)

1. A ballastless track simulation adjustment calculation method is characterized in that, calculating the simulation adjustment of the plane reference rail comprises the following steps: Step A1: read in the design abscissa and measured abscissa at each detection point of the track; Step A2: Calculate the difference between the designed abscissa and the measured abscissa at each detection point of the track to obtain the lateral offset of the track at each detection point; Step A3: Carry out polynomial fitting to the lateral offset of the track, and fit the simulation curve function; Step A4: Bring the mileage of the detection point into the simulation curve function and calculate the simulation curve function value; Step A5: Calculate the difference z between the simulated curve function value and the corresponding track lateral offset to obtain the simulated adjustment amount; Step A6: First calculate the sum of the orbital lateral offset and the simulated adjustment, and use it as the new orbital lateral offset; then repeat steps A3-A5 until the simulated adjustment obtained in step A5 is 0; , adding the simulated adjustments calculated in step 5 in each round to obtain the simulated adjustments of the plane reference rail at this place. 2. The ballastless track simulation adjustment amount calculation method according to claim 1, characterized in that, in the step 3, the specific steps of fitting the simulation curve function are as follows: a1): Carry out polynomial fitting of different orders to the lateral offset of the track to obtain simulated curves of different orders; and analyze the smoothness of the simulated curves of different orders; a2): Analyze the smoothness of simulation curves of different orders: First, calculate the first-order derivative y' and the second-order derivative y" of the simulation curves of different orders; Then, calculate the radius of curvature of the simulated curves of different orders according to the following formula: <mrow> <mi>&amp;rho;</mi> <mo>=</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <msup> <mi>y</mi> <mrow> <mo>&amp;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>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mo>|</mo> </mrow> </mfrac> </mrow> Finally, the smoothness of the simulated curves of different orders is judged according to the size of the curvature radius ρ. The larger the curvature radius, the higher the curvature, that is, the higher the smoothness of the curve; a3): Use the following formula to evaluate the approximation δ of the simulation curves of different orders: <mrow> <mi>&amp;delta;</mi> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>m</mi> </munderover> <msup> <mrow> <mo>&amp;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>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> </mrow> Wherein, P( _xi ) represents the function value of the simulation curve, and y _represents the lateral offset of the track before adjustment; a4): Combining the results of step a2) and step a3), the order of the simulation curve is determined based on the principle of high smoothness and high approximation, so as to fit the simulation curve function. 3. The method for calculating the simulated adjustment amount of the ballastless track according to claim 1, characterized in that, in the step A5, the simulated adjustment amount is the closest to z and is an integer multiple of 0.5 mm or 1 mm. 4. A ballastless track simulation adjustment calculation method is characterized in that the calculation of the simulation adjustment of the elevation reference rail comprises the following steps: Step B1: read in the design ordinate and measured ordinate at each detection point of the track; Step B2: Calculate the difference between the design ordinate and the measured ordinate at each detection point of the track to obtain the longitudinal offset of the track at each detection point; Step B3: Carry out polynomial fitting to the longitudinal offset of the track, and fit the simulation curve function; Step B4: Bring the mileage of the detection point into the simulation curve function and calculate the value of the simulation curve function; Step B5: Calculate the difference between the simulated curve function value and the corresponding track longitudinal offset to obtain the simulated adjustment amount, which should be an integer multiple of 0.5mm or 1mm; Step B6: First calculate the sum of the track longitudinal offset and the simulated adjustment, and use it as the new track longitudinal offset; then repeat steps B3-B5 until the simulated adjustment obtained in step B5 is 0. , the simulated adjustments calculated in step B5 in each round are added to obtain the simulated adjustments of the elevation reference rail at this place. 5. The ballastless track simulation adjustment amount calculation method according to claim 4, characterized in that, in the step 3, the specific steps of fitting the simulation curve function are as follows: b1): Carry out polynomial fitting of different orders to the lateral offset of the track, and obtain simulation curves of different orders; b2): Analyze the smoothness of the simulation curves of different orders; The method for smoothness of the simulated curves of different orders of analysis is: First, calculate the first-order derivative y' and the second-order derivative y" of the simulation curves of different orders; Then, calculate the radius of curvature of the simulated curves of different orders according to the following formula: <mrow> <mi>&amp;rho;</mi> <mo>=</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <msup> <mi>y</mi> <mrow> <mo>&amp;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>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mo>|</mo> </mrow> </mfrac> </mrow> Finally, the smoothness of the simulated curves of different orders is judged according to the size of the curvature radius ρ. The larger the curvature radius, the higher the curvature, that is, the higher the smoothness of the curve; b3): Use the following formula to evaluate the approximation degree δ of the simulation curves of different orders: <mrow> <mi>&amp;delta;</mi> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>m</mi> </munderover> <msup> <mrow> <mo>&amp;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>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> </mrow> Wherein, P( _xi ) represents the function value of the simulation curve, and y _represents the longitudinal offset of the track before adjustment; b4): Combining the results of step b2) and step b3), the order of the simulation curve is determined based on the principle of high smoothness and high approximation, so as to fit the simulation curve function. 6. The method for calculating the simulated adjustment amount of the ballastless track according to claim 4, characterized in that, in the step B5, the simulated adjustment amount is the closest to z and is an integer multiple of 0.5 mm or 1 mm. 7. A fine-tuning method for ballastless track, characterized in that, first, calculate the simulated adjustment amount of the plane reference rail at each position of the ballastless track according to the method described in claims 1 to 3; Calculate the simulated adjustment amount of the elevation reference rail at each position of the ballastless track; then, adjust the track fasteners and backing plates at the corresponding positions of the ballastless track according to the calculated simulated adjustment amount of the plane reference rail and the simulated adjustment amount of the elevation reference rail .