Rail adjustment amount calculation method

Abstract

The present application belongs to the technical field of track measurement data processing, and particularly relates to a track adjustment amount calculation method. Firstly, track deviation data varying with mileage is obtained, all extreme points greater than a first threshold value are screened out, and all the screened extreme points are taken as internal nodes of a cubic spline curve. Then, the starting point and the ending point of the screened internal nodes are taken as boundary nodes, the first derivative of the boundary nodes is set to zero, and thus a cubic spline curve fitting with fixed boundary conditions is performed. Finally, track adjustment amount calculation is performed according to the fitted cubic spline curve. The present application can fully take into account systematic track deviation, significantly reduce the size of track adjustment amount under the premise of ensuring track smoothness, improve track fine adjustment efficiency, and can be popularized and used in track transportation railway smoothness maintenance such as high-speed railway, general speed railway and subway.

Description

Technical Field

[0001] This invention belongs to the field of track measurement data processing technology, and specifically relates to a method for calculating track adjustment. Background Technology

[0002] The rapid and scientific calculation of track adjustment is one of the key technologies for maintaining high track smoothness in railways, and scholars both domestically and internationally have conducted extensive research in this area. For example, the article "Research on Automatic Calculation Method of Simulated Adjustment of Ballastless Track Reference Rail" published by Nie Songguang, Wu Dijun, et al. in the 2016 issue of the *Journal of Railway Science and Engineering* (Volume 13, Issue 7) proposes a polynomial fitting method for calculating track adjustment. However, the polynomial degree needs to be manually selected based on the specific scenario, and its application effectiveness depends on the knowledge level of the technicians. The article "Application of Wavelet Transform in Fine Adjustment of High-Speed ​​Railway Track" published by Zhao Long, Lu Jiankang, et al. in the 2017 issue of the *Journal of Railway Engineering* (Volume 34, Issue 04) applies wavelet transform to track adjustment calculation. However, this method does not consider the situation where local track deviations consistently exceed limits, and its theory is complex and difficult to program. The authors Li Yangtenglong, Cen Minyi, et al. published an article titled "Optimization Algorithm for Fine Adjustment of Ballastless Track Rails in High-Speed ​​Railways" in the *Journal of Wuhan University (Information Science Edition)*, Volume 43, Issue 6, 2018. This article proposed an automatic calculation method for track adjustment based on the L1 norm optimality principle; however, this method suffers from low computational efficiency and still cannot meet the requirements of practical engineering. Li Jimin, in his 2012 master's thesis "Design and Application of Track Fine Adjustment System Based on Genetic Algorithm," disclosed the use of a genetic algorithm for track adjustment calculation; however, this method cannot guarantee a globally optimal track adjustment scheme. The authors Liu Jiaqi, Yu Chaogang, et al. published an article titled "Research on Track Fine Adjustment Optimization Based on Improved PSO-GA Algorithm" in the *Intelligent Computer and Applications*, Volume 11, Issue 12, 2021. This article proposed an improved particle swarm optimization-genetic algorithm suitable for track fine adjustment to address the problems of excessively large local track adjustment amounts and low computational efficiency; however, this method is theoretically complex and still cannot completely avoid the problem of local optima. None of these methods can obtain a truly optimal track adjustment scheme. Summary of the Invention

[0003] The purpose of this invention is to provide a method for calculating track adjustment amount, so as to solve the problem that the existing technology cannot obtain a better track adjustment amount.

[0004] To solve the above-mentioned technical problems, the present invention provides a method for calculating track adjustment, comprising the following steps:

[0005] 1) Obtain track deviation data that varies with mileage, filter out all extreme points that are greater than the first threshold, and use all the filtered extreme points as the internal nodes of the cubic spline curve;

[0006] 2) Use the starting and ending points of the selected internal nodes as boundary nodes, and set the first derivative of the boundary nodes to zero, i.e. Where S1′(m1) represents the first derivative of the cubic polynomial function in the first subinterval at the starting point boundary point, S n ′(m n+1 ) represents the first derivative of the cubic polynomial function in the nth subinterval at the termination boundary point, where n represents the total number of intervals, and d1′ = d′. n+1 =0, thus performing cubic spline curve fitting under fixed boundary conditions;

[0007] 3) Calculate the track adjustment amount based on the fitted cubic spline curve.

[0008] Its beneficial effects are as follows: This invention uses cubic spline curve fitting to process the acquired track deviation data that varies with mileage. The cubic spline curve used specifically refers to a cubic spline curve that satisfies the best approximation property under fixed boundary conditions. During fitting, only the extreme points where the absolute value of the track deviation exceeds a certain threshold are used as internal nodes. This fully utilizes the characteristic that the first derivative of the track deviation curve is zero at the extreme points, further improving the smoothness of the fitted curve. This invention can fully consider the systematic deviation of the track system, significantly reducing the amount of track adjustment while ensuring track smoothness, and improving the efficiency of track fine-tuning. It can be widely used in the maintenance of railway smoothness in high-speed railways, conventional railways, subways, and other rail transit systems.

[0009] Furthermore, the track deviation data obtained in step 1) is the track deviation data after gross error removal.

[0010] Its beneficial effects are: it removes gross errors from track deviation data and improves the smoothness of the fitted curve.

[0011] Furthermore, after step 1), it is necessary to determine whether the absolute value of the orbital deviation corresponding to the selected extreme point exceeds the second threshold. If it exceeds the second threshold, the orbital deviation of the extreme point that exceeds the second threshold will be limited to the second threshold.

[0012] Its beneficial effect is that setting a second threshold can prevent situations where the track deviation is still greater than the relevant specification requirements after track fine-tuning.

[0013] Furthermore, the second threshold is less than the track deviation required by the railway.

[0014] Furthermore, the condition equations used in step 2) for fitting cubic spline curves with fixed boundary conditions include:

[0015]

[0016] In the formula, i is taken from [1, n]; S i () and S i+1 () denote the cubic polynomial functions of the i-th and (i+1)-th subintervals, respectively; S i ′() and S′ i+1 () denote the first derivatives of the cubic polynomial functions in the i-th and (i+1)-th subintervals, respectively; S i "() and S" i+1 () denote the second derivatives of the cubic polynomial functions in the i-th and (i+1)-th subintervals, respectively; m j This represents the mileage corresponding to the j-th internal node.

[0017] Furthermore, the error equation used in step 2) for fitting cubic spline curves with fixed boundary conditions is:

[0018]

[0019] In the formula, m j d represents the mileage corresponding to the j-th internal node; j This represents the orbital deviation corresponding to the j-th internal node; v j Represents the model residuals; a i b i c i and d i Let represent the coefficients of the cubic polynomial in the i-th subinterval.

[0020] Furthermore, the condition equations used in step 2) for fitting cubic spline curves with fixed boundary conditions also include: S i ′(m j ) = 0.

[0021] Furthermore, the first threshold is the median or average of all extreme points in the orbital deviation data. Detailed Implementation

[0022] Extensive practical experience has demonstrated a significant spatial correlation in track deviation (referring to deviations in baseline elevation or lateral deviation), primarily determined by the track's structural characteristics and construction methods. Furthermore, discrete track deviation data, plotted with mileage on the horizontal axis and track deviation (positive for left deviation and negative for right deviation) on the vertical axis, can be viewed as discrete sampling of a curve that continuously varies with track mileage. Although deviations exist between the actual track alignment and the design alignment from a microscopic (small-scale) perspective, they generally match the design alignment from a macroscopic (large-scale) perspective. Therefore, the track deviation curve inevitably exhibits multiple extrema; positive extrema are called peaks, and negative extrema are called troughs; both are collectively referred to as track deviation extreme points.

[0023] If extreme points of track deviation exceeding a certain threshold are used as internal nodes of a spline curve for cubic spline curve fitting, the fitted curve will better reflect the main characteristics of the track deviation curve. Furthermore, using the fitted curve as a baseline for track fine-tuning will significantly reduce the amount of track adjustment. That is, if the fitted curve can best approximate the track deviation curve, the amount of track adjustment will be minimized. Therefore, the cubic spline curve used in this invention specifically refers to a cubic spline curve that satisfies the best approximation property under fixed boundary conditions. Moreover, this invention, by using only extreme points where the absolute value of the track deviation exceeds a certain threshold as internal nodes, fully utilizes the characteristic that the first derivative of the track deviation curve is zero at the extreme points to further improve the smoothness of the fitted curve.

[0024] The present invention will now be described in detail with reference to the embodiments.

[0025] Example of track adjustment calculation method:

[0026] An embodiment of the track adjustment calculation method of the present invention is as follows:

[0027] Step one involves removing outliers from the acquired orbital deviation data. After outlier removal, extreme points exceeding a first threshold ε1 are identified and used as internal nodes of the cubic spline curve. The first threshold ε1 in this step controls the density of internal nodes, ensuring that the fitted cubic spline curve reflects only the main characteristics of the orbital deviation curve. Here, the first threshold ε1 can be the median or average of all extreme points.

[0028] Step two: Determine if the absolute value of the track deviation at the inner node exceeds the second threshold ε2. If it does, set its absolute value to the second threshold ε2, keeping the sign unchanged. This process is the amplitude limiting process. The purpose of the second threshold ε2 in this step is to prevent the track deviation from exceeding the relevant specifications after fine-tuning. It is generally set slightly less than the specification limit. For example, for high-speed railways requiring track deviation to be no more than 10mm, the second threshold ε2 can be set to approximately 8mm.

[0029] Step 3: Using the selected start and end points of the internal nodes as boundary nodes, and applying fixed boundary (Type I boundary) conditions, while ensuring that the first derivative of the internal nodes is zero, perform cubic spline curve fitting under fixed boundary conditions. The specific process is as follows:

[0030] Since a cubic spline function is a piecewise function composed of piecewise cubic polynomials, we know that the function S in any interval... i (m) are all cubic polynomial functions:

[0031] S i (m)=ai +b i (m-m0)+c i (m-m0) 2 +d i (m-m0) 3 (i = 1, 2, ..., n) (1)

[0032] In the formula, i represents the sub-interval number; S i () represents a cubic polynomial function for the i-th subinterval; a i b i c i and d i The coefficients of the cubic polynomial in the i-th sub-interval are the parameters to be estimated; m represents the line mileage; m0 represents the starting mileage of the corresponding sub-interval.

[0033] Based on the continuity of the function values, first derivative, and second derivative of the cubic spline function at the interior nodes, the following conditional equations can be established:

[0034]

[0035] In the formula, j represents the internal node number, m j Let S' represent the mileage corresponding to the j-th internal node; S' represent the first derivative of the function; and S'' represent the second derivative of the function. Clearly, 3n-3 equations can be derived from n-1 points.

[0036] Based on the fixed boundary conditions, two conditional equations can be derived by setting the first derivative values ​​of the boundary nodes:

[0037]

[0038] In the formula, S1′(m1) represents the first derivative of the cubic polynomial function in the first subinterval at the initial (first) boundary node; S n ′(m n+1 ) represents the first derivative of the cubic polynomial function in the nth subinterval at the terminal (tail) boundary node; d1′ and d′ n+1 The first derivative value at the beginning and end boundary nodes is artificially set. Obviously, the first derivative value at the beginning and end boundary nodes is usually unknown. Therefore, this invention selects the extreme point of the trajectory deviation as the beginning and end boundary nodes, where d1′=d′. n+1 =0.

[0039] Considering the condition that the internal nodes are extreme points, the conditional equations are as follows:

[0040] S i ′(m j )=0 (4)

[0041] Using orbital point data, construct the error equation:

[0042]

[0043] In the formula, (m j ,d j ) represents the track deviation data (mileage and deviation) for track point j; v j This represents the model residuals.

[0044] In summary, the functional model for fitting cubic spline curves with fixed boundary conditions includes conditional equations and error equations. It is a conditional parametric adjustment model, which can be solved using the conditional parametric adjustment method. The specific process will not be elaborated here.

[0045] Step four: Using the fitted cubic spline curve as the baseline for track fine-tuning, calculate the adjustment amount for each track point to obtain the track adjustment scheme.

[0046] In summary, this invention constructs a function model for fitting cubic spline curves and outlines the solution method. This invention fully considers systematic deviations in the track system, significantly reducing the amount of track adjustment while ensuring track smoothness, thus improving the efficiency of track fine-tuning. This invention can be widely applied to the maintenance of track smoothness in high-speed railways, conventional railways, subways, and other rail transit systems.

[0047] Furthermore, the method described above can be implemented using computer program code. For example, a trajectory adjustment calculation device can be designed, comprising a memory, a processor, and an internal bus. The processor and memory communicate and interact with each other via the internal bus. The memory includes at least one software functional module stored in the memory. The processor executes various functional applications and data processing by running the software program and modules stored in the memory, thereby realizing the trajectory adjustment calculation method of the present invention. The processor can be a microprocessor (MCU), a programmable logic device (FPGA), or other processing devices. The memory can be various types of memory that store information using electrical energy, such as RAM and ROM; it can also be various types of memory that store information using magnetic energy, such as hard disks, floppy disks, magnetic tapes, magnetic core memory, bubble memory, and USB flash drives; it can also be various types of memory that store information using optical methods, such as CDs and DVDs; and of course, it can also be other types of memory, such as quantum memory and graphene memory.

Claims

1. A method for calculating track adjustment amount, characterized in that, Includes the following steps: 1) Obtain track deviation data that varies with mileage, filter out all extreme points that are greater than the first threshold, and use all the filtered extreme points as the internal nodes of the cubic spline curve; 2) Use the start and end points of the selected internal nodes as boundary nodes, and set the first derivative of the boundary nodes to zero, i.e. ,in Let be the first derivative of the cubic polynomial function within the first subinterval at the starting point and boundary points. For the first The first derivative of a cubic polynomial function over a subinterval at the termination boundary point. Given the total number of intervals, and based on the continuity of the function values, first derivative, and second derivative of the cubic spline function at the interior nodes, as well as the fact that the interior nodes are extreme points, corresponding conditional equations are established to perform cubic spline curve fitting under fixed boundary conditions; and the error equation used in the fitting process is: , The first Mileage and track deviation corresponding to each node; For model residuals; , , and For the first The coefficients of the cubic polynomial in each subinterval; 3) Calculate the track adjustment amount based on the fitted cubic spline curve.

2. The method for calculating track adjustment amount according to claim 1, characterized in that, The track deviation data obtained in step 1) is the track deviation data after gross error removal.

3. The method for calculating track adjustment amount according to claim 1, characterized in that, After step 1), it is necessary to determine whether the absolute value of the track deviation corresponding to the selected extreme point exceeds the second threshold. If it exceeds the second threshold, the track deviation of the extreme point that exceeds the second threshold will be limited to the second threshold.

4. The method for calculating track adjustment amount according to claim 3, characterized in that, The second threshold is less than the track deviation required by the railway.

5. The method for calculating track adjustment amount according to claim 1, characterized in that, The conditional equations corresponding to the continuity of the function values, first derivative, and second derivative of a cubic spline function at its interior nodes are as follows: In the formula, from Iterate through the data to retrieve values; and They represent the first The and the first A cubic polynomial function over a subinterval; and They represent the first The and the first The first derivative of a cubic polynomial function over a subinterval; and They represent the first The and the first The second derivative of a cubic polynomial function over a subinterval; Indicates the first The mileage corresponding to each internal node.

6. The method for calculating track adjustment amount according to claim 1, characterized in that, The conditional equations corresponding to internal nodes being extreme points are: .

7. The method for calculating track adjustment amount according to claim 1, characterized in that, The first threshold is the median or average of all extreme points in the orbital deviation data.

8. The method for calculating track adjustment amount according to claim 4, characterized in that, The railway requires a track deviation of 10mm, with a second threshold of 8mm.

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