A high-speed railway vertical curve dynamic long-wave unevenness optimization method

Abstract

The application discloses a high-speed railway vertical curve dynamic long-wave unevenness optimization method, comprising the following steps: obtaining a newly-built line or an operation line route profile and parameters thereof, determining an initial transition curve mathematical model and the length and the circular curve radius of the initial transition curve line type according to preset high-speed railway dynamic detection filtering and / or driving dynamics indexes, and adding the initial transition curve line type to the head and tail of the route profile circular curve, constructing constraint conditions according to the newly-built line or the operation line profile characteristics, solving all vertical curve optimization parameters of the profile satisfying the constraint conditions, and designing and constructing according to actual engineering conditions. The application has wide application range, can effectively eliminate the sudden change of the vertical acceleration of the train body when the high-speed train passes through the head and tail of the profile circular curve, can weaken the long-wave unevenness of the dynamic detection high-low 120m and above of the head and tail of the high-speed railway circular curve, and effectively improves the dynamic vertical smoothness of the high-speed railway.

Description

Technical Field

[0001] This invention relates to the field of high-speed railway line alignment design and operation and maintenance technology, and in particular to a method for optimizing the dynamic long-wave irregularities of vertical curves in high-speed railways. Background Technology

[0002] As train speeds increase, researchers have begun to study the optimization of vertical curves in longitudinal profiles. During the design phase of new railway lines, patent document CN113742812A discloses the use of half-wave sinusoidal curves and quartic curves between adjacent gradients to eliminate vertical impact between the wheel and rail at connection points. Patent document CN109165427A discloses a method for optimizing longitudinal profiles for high-speed railways in operation, proposing multi-slope fitting and radius adjustment. The paper "Optimization of Vertical Curve Smoothness and Engineering Application in High-Speed ​​Railways" discloses improving longitudinal profile smoothness by increasing the radius of circular curves.

[0003] However, the aforementioned existing technologies have the following drawbacks: Patent document CN113742812A is only applicable to the longitudinal profile design of newly built lines and not to operating lines; for high-speed railways already in operation, patent document CN109165427A cannot solve the problem of unevenness of the long waves at the beginning and end of the vertical curve by fitting multiple slope sections; the method of increasing the radius of the circular curve cannot eliminate the problem of vertical speed change, and considering the difficulty of on-site construction and maintenance, the radius of the circular curve can be increased in a very limited way, especially for convex slope change points, where the increase in radius is not feasible due to the limitation of the amount of track that can be dropped. In particular, the current achievements in improving the unevenness of vertical curves at the beginning and end of operational lines are mainly technical summaries or experience generalizations based on individual engineering tests. The changed longitudinal profile alignment has not been tested by high-speed railway dynamic detection filtering or train dynamics testing, nor by static 300m chord elevation index testing. It only reduces the elevation and long wave amplitudes of the track in specific test sections to below the acceptance index after dynamic testing by high-speed railway comprehensive inspection vehicles. The goal is to avoid any points deduction. Not only has the dynamic and static unevenness of the longitudinal profile not been thoroughly rectified, but it has also caused distortion of the track's static geometry and alignment in the high-speed railway maintenance records, which will create difficulties for the high-speed railway maintenance department in subsequent scientific maintenance and management.

[0004] Therefore, the applicant has invented a method for optimizing the dynamic long-wave irregularities of vertical curves in high-speed railways to solve the above problems. Summary of the Invention

[0005] This invention proposes a dynamic long-wave irregularity optimization method for vertical curves in high-speed railways to solve the problem that existing methods for designing and maintaining vertical curves in the longitudinal profile of high-speed railways cannot be applied to both newly built and operational lines. This results in abrupt changes in the vertical acceleration detected by dynamic detection at the beginning and end of the vertical curve, causing long-wave irregularities of more than 120m in track elevation.

[0006] The present invention achieves the above objectives through the following technical solutions:

[0007] This invention provides a method for optimizing the dynamic long-wave irregularities of vertical curves in high-speed railways, comprising:

[0008] Obtain the longitudinal profile type of the line, the longitudinal profile parameters corresponding to the longitudinal profile type of the line, and the transition curve to be selected. The longitudinal profile type of the line is either a newly built line longitudinal profile or an operating line longitudinal profile.

[0009] Based on the preset dynamic detection filtering and / or train dynamics indicators for high-speed railways, the vertical curves of the longitudinal profile of the line after adding each transition curve are filtered and / or dynamically tested respectively. Based on the results of each filtering and / or test, the vertical curve of the longitudinal profile of the line that satisfies the minimum amplitude of high and low long wave irregularities and / or the optimal smoothness under actual engineering conditions is selected as the initial vertical curve of the longitudinal profile of the line. The longitudinal profile parameters of the initial vertical curve of the longitudinal profile of the line are used as the parameters to be optimized.

[0010] Select preset constraint conditions according to the type of longitudinal profile of the line. When the type of longitudinal profile of the line is a newly built line, the constraint conditions include minimum slope length constraint and constraint that the vertical curve does not coincide with the horizontal transition curve. When the type of longitudinal profile of the line is an operating line, the constraint conditions include track vertical adjustability or track lifting amount constraint, minimum slope length constraint and constraint that the vertical curve should not coincide with the horizontal transition curve.

[0011] Based on the parameters to be optimized and the initial longitudinal profile vertical curve, solve for the longitudinal profile vertical curves corresponding to all longitudinal profile parameters that satisfy the constraints. Through preset high-speed railway dynamic detection filtering and / or train dynamics indices, filter and / or test the longitudinal profile vertical curves corresponding to all parameters that satisfy the constraints one by one. Select the longitudinal profile parameter that satisfies one or more of the following conditions under actual engineering conditions: minimum amplitude of track elevation and low long-wave irregularity, optimal smoothness, and optimal train dynamics indices, as the optimal solution.

[0012] Obtaining the longitudinal profile parameters corresponding to the longitudinal profile type of the line includes:

[0013] When the longitudinal profile type of the line is a newly built line longitudinal profile, the longitudinal profile design parameters obtained according to the high-speed railway design specifications are used as the longitudinal profile parameters. The longitudinal profile design parameters include the elevation of the slope change point, the slope length, and the radius of the circular curve.

[0014] When the longitudinal profile type of the line is an operational line longitudinal profile, the actual elevation of the longitudinal profile is precisely measured, and the longitudinal profile fitting parameters are obtained based on the actual elevation of the longitudinal profile as longitudinal profile parameters. The longitudinal profile fitting parameters include the elevation of the slope change point, the slope length, and the radius of the circular curve.

[0015] Based on preset dynamic detection filtering and / or train dynamics indicators for high-speed railways, the vertical curves of the longitudinal profile of the line after the addition of each transition curve are subjected to filtering processing and / or dynamic testing, including:

[0016] Based on the selected transition curve, the longitudinal profile type of the line, and the longitudinal profile type of the line, calculate the mathematical model of each transition curve and its length and radius of the circular curve. The mathematical model of the transition curve includes a cubic parabola mathematical model, a quintic parabola mathematical model, a seventh parabola mathematical model, a half-wave sine mathematical model, a one-wave sine mathematical model, and a seventh-order quadrilateral mathematical model.

[0017] Calculate the mathematical model of each transition curve, its length, and the radius of the circular curve, and add the transition curve to the vertical curve of the longitudinal profile of the line to obtain the vertical curve of the longitudinal profile of the line after adding the transition curve;

[0018] By using preset high-speed railway dynamic detection filtering indicators and / or train dynamics indicators, the vertical curves of the longitudinal profile of the line after the addition of each transition curve are filtered and / or dynamically tested.

[0019] The mathematical model for the transition curve includes:

[0020] Mathematical model of a cubic parabola:

[0021]

[0022] Mathematical model of a quintic parabola:

[0023]

[0024] Mathematical model of a seventh parabola:

[0025]

[0026] Half-wave sine mathematical model:

[0027]

[0028] A wave of sinusoidal mathematical models:

[0029]

[0030] Seventh-degree quaternion mathematical model:

[0031]

[0032] In the formula, l0 is the length of the transition curve, R0 is the radius of the circular curve, and x and y are the coordinates in the local coordinate system of the mathematical model of the transition curve. The local coordinate system takes the starting point of the transition curve as the origin, the tangent line through the starting point as the x-axis, the growth direction of the transition curve as the positive direction, the perpendicular x-axis through the starting point as the y-axis, and the bending direction of the transition curve as the positive direction of the y-axis.

[0033] In the constraints:

[0034] The minimum slope length constraint is:

[0035]

[0036] The constraint that the vertical curve does not coincide with the planar transition curve is:

[0037]

[0038] The vertical adjustability constraint of the track is:

[0039]

[0040] Where L represents the length of the slope, K BP1 and K BP2 Let R0 be the horizontal mileage of two adjacent slope change points, R0 be the radius of the circular curve, and Δi be the algebraic difference (‰) between adjacent slopes. max The maximum absolute value of Δi is given, V is the design speed, and K is the maximum value of Δi. BP K is the horizontal mileage of the slope change point. Star / End Here, is the starting or ending mileage of the horizontal transition curve, T is the tangent length after the addition of the transition curve alignment, p is the internal displacement, y0 is the y-coordinate of the transition curve's ending point, β0 is the tangent angle of the transition curve's ending point, v(K) represents the track's vertical deviation, χ(K) and ζ(K) represent the lower and upper limits of the actual adjustable amount of the track, respectively, and H... desi (K) represents the design elevation of the vertical curve of the longitudinal profile of the operating line after the addition of the transition curve alignment; H meas (K) represents the actual elevation of the vertical curve of the longitudinal profile of the operating line, and the track vertical deviation v(K) is related to the mileage K and the elevation H of the gradient change point. BP The design elevation is a nonlinear function of the radius R0 of the circular curve and the length l0 of the transition curve. The design elevation includes the design elevation of the front and back slope sections, the design elevation of the circular curve, the design elevation of the first transition curve, and the design elevation of the second transition curve. The first transition curve is the transition curve between the front slope section and the circular curve, and the second transition curve is the transition curve between the circular curve and the back slope section.

[0041] When the design elevation is the same as the design elevation of the front and rear slope sections, the design elevation H desi The formula for calculating (K) is:

[0042]

[0043] In the formula K BP and H BP Let K be the horizontal mileage and elevation of the slope change point, K be the mileage of any point on the slope segment, and i be the slope of the slope segment corresponding to mileage K. ZH K represents the distance between the straight and gentle curve points on a vertical curve. HZ Indicates the mileage of the transition point between vertical and straight sections;

[0044] When the design elevation is the same as the design elevation of the circular curve, the design elevation H desi The formula for calculating (K) is:

[0045]

[0046] In the formula, p is the inner displacement, R0 is the radius of the circular curve, and H... desi In formula (K), "±" is used for concave vertical curves and "−" is used for convex vertical curves. HY K represents the mileage of the transition point of the vertical curve. YH This indicates the mileage of the transition point of the vertical curve.

[0047] When the design elevation is the design elevation of the transition curve, any mileage K and design elevation H desi (K) is calculated using the following formula:

[0048]

[0049] In the formula, T is the length of the vertical tangent of the longitudinal profile after the addition of the transition curve, i is the slope at the starting point of the transition curve (in‰), and K and H... desi (K) takes the sign of ± for the first fractional term, + for the first transition curve, and - for the second transition curve; K and H desi The second term of (K) is a fraction with "±", concave vertical curves take "+", and convex vertical curves take "−".

[0050] The high-speed railway dynamic detection filtering includes: passband cutoff wavelength ≥120m, maximum passband attenuation -3dB, and stopband minimum slope of 24dB / octave. The train dynamics indicators include: derailment coefficient ≤0.8, wheel load reduction rate ≤0.6, and vertical vibration acceleration of the car body ≤2.5m / s². 2 Sperling comfort index ≤ 2.5.

[0051] The passband cutoff wavelengths include 120m, 150m, 200m and >200m.

[0052] The actual engineering conditions include:

[0053] Measurement technical conditions, which refer to the accuracy indicators that can be achieved by using measurement equipment to measure the actual elevation of the longitudinal profile of the line;

[0054] Construction technical conditions, when the track structure of the line is ballasted track, include but are not limited to the longitudinal height and low operation accuracy of the tamping machine and the maximum track lifting volume limit; when the track structure of the line is ballastless track, the construction technical conditions include but are not limited to the sleeper fastener pad grade difference and its remaining adjustable amount.

[0055] The beneficial effects of this invention are as follows:

[0056] 1. The present invention provides a method for optimizing the dynamic long-wave irregularity of vertical curves in high-speed railways, which solves the problem that the existing methods for designing and maintaining vertical curves in the longitudinal profile of high-speed railways cannot be applied to both newly built and operating lines at the same time, and the obtained dynamic track smoothness has not been tested by dynamic filtering and / or train dynamics testing of high-speed railways. This results in abrupt changes in the vertical acceleration detected by dynamic detection of high-speed railways at the beginning and end of the vertical curves in the longitudinal profile, causing long-wave irregularities of more than 120m in height difference on the operating track.

[0057] 2. The optimized longitudinal profile of the line in this invention will be more conducive to the consistency of dynamic and static smoothness indicators of high-speed railway tracks, reduce wheel and rail wear and maintenance workload of operating lines, and improve the technical level of track operation, maintenance and management.

[0058] 3. The addition of a transition curve in the longitudinal profile not only makes the transition between straight lines and circular curves smoother, but also allows for a moderate reduction in the radius of the circular curve in the route selection design, increasing the flexibility to adapt to terrain undulations, reducing project costs, and making the high-speed railway line run more smoothly at high speeds after completion; it also makes the long-wave smoothness of the track elevation of the operating line higher, further improving the stability and comfort of passengers riding high-speed railway trains.

[0059] 4. It is applicable not only to ballastless tracks of high-speed railways, but also to ballasted tracks of high-speed railways.

[0060] 5. Adjust relevant parameters according to the dynamic detection filtering wavelength and / or train dynamics indicators and their design specifications for conventional railways, urban rail transit and underground railways. This invention is also applicable to the optimization of long-wave irregularities in the dynamic detection of vertical curves in the longitudinal profile of conventional railways, urban rail transit and underground railways. Attached Figure Description

[0061] Figure 1 This is a schematic diagram of the vertical curve of the longitudinal section of an embodiment of the present invention, in which a transition curve is added;

[0062] Figure 2 This is a schematic diagram of the easing curve in an embodiment of the present invention;

[0063] Figure 3 This is a schematic diagram of the vertical adjustment of the track after adding a transition curve in an embodiment of the present invention;

[0064] Figure 4 This is an illustration of the calculation of the horizontal mileage and elevation of the transition curve in an embodiment of the present invention;

[0065] Figure 5 This is a schematic diagram comparing the vertical acceleration before and after adding the transition curve in an embodiment of the present invention;

[0066] Figure 6 This is a partial horizontal and vertical profile design of a newly built high-speed railway in an embodiment of the present invention;

[0067] Figure 7 In this embodiment of the invention, different gradient curves are added to make the track uneven with long waves of varying heights.

[0068] Figure 8 In this embodiment of the invention, a transition curve is added to the longitudinal profile of a newly constructed high-speed railway line for high-speed rail line elevation and low-frequency long-wave contrast.

[0069] Figure 9 The diagram below shows the concave and convex vertical curve segments selected in the embodiments of the present invention (9(a) and 9(b) represent concave and convex vertical curve segments, respectively).

[0070] Figure 10 This is a schematic diagram of the measured elevation and fitting deviation of the longitudinal profile in an embodiment of the present invention (10(a) and 10(b) represent the measured elevation and fitting deviation of the concave and convex vertical curve segments, respectively).

[0071] Figure 11 This is a schematic diagram showing the results of verifying the selected transition curve shape using the 120m high-speed railway dynamic detection filter cutoff wavelength in an embodiment of the present invention (11(a) and 11(b) represent the peak value and standard deviation of the irregularity, respectively).

[0072] Figure 12 This is a schematic diagram of the vertical adjustment amount of the track after adding a transition curve in an embodiment of the present invention (12(a) and 12(b) respectively show the schematic diagram of the vertical adjustment amount of the track after adding a transition curve to the concave and convex vertical curve segments).

[0073] Figure 13 This is a schematic diagram of the unevenness of the vertical curve in the longitudinal section after the dynamic detection filter cutoff wavelength verification and optimization design of the 120m high-speed railway in an embodiment of the present invention (13(a) and 13(b) represent schematic diagrams of the unevenness of the vertical curve in the longitudinal section after the optimization design of the concave and convex vertical curve segments, respectively).

[0074] Figure 14 The above are schematic diagrams comparing the track elevation and long-wave irregularities before and after adding the transition curve in the embodiments of the present invention (14(a) and 14(b) respectively represent schematic diagrams comparing the track elevation and long-wave irregularities before and after adding the transition curve in the vertical curve segment of the concave and convex longitudinal sections). Detailed Implementation

[0075] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0076] In this invention, the terms "first," "second," etc., are used only for distinguishing descriptions and should not be construed as indicating or implying relative importance.

[0077] For newly built high-speed railway lines:

[0078] During the route selection and design phase, the connection between the preceding and following slope sections is designed using transition curves, circular curves, and other transition curves, and this is applied during construction. For lines with different design speeds, the minimum circular curve radius, minimum slope length, and distance between the slope change point and the start and end points of the horizontal transition curve in the longitudinal profile of the line should meet the requirements of the high-speed railway design specifications. The main steps of the implementation plan are as follows:

[0079] The specific details of each step are as follows:

[0080] Q1. Determine longitudinal profile parameters

[0081] For newly constructed lines, the parameters of each longitudinal section are determined according to the relevant requirements of high-speed railway design specifications, specifically including the slope i‰ and the elevation H of the slope change points for each longitudinal section. BP , slope length, and radius of the circular curve R0.

[0082] Q2. Determine the initial transition curve shape.

[0083] Based on the filtering and / or dynamic test results, the transition curve shape with the minimum amplitude of high and low long-wave irregularities and / or optimal smoothness is selected. Combining the longitudinal profile parameters obtained from Q1 and the selected transition curve shape, the initial transition curve shape for each line's longitudinal profile is determined through dynamic detection filtering (filter cutoff wavelength ≥ 120m) and / or dynamic testing on high-speed railways. This initial transition curve shape serves as the initial transition curve shape for each line's longitudinal profile. The main design parameters for dynamic detection filtering on high-speed railways are as follows: ① Passband cutoff wavelength ≥ 120m; ② Maximum passband attenuation -3dB; ③ Minimum stopband slope of 24dB / octave. Passband cutoff wavelengths include 120m, 150m, 200m, and longer wavelengths. The main design parameters for train dynamics are as follows: derailment coefficient ≤ 0.8, wheel load reduction rate ≤ 0.6, and vertical vibration acceleration of the car body ≤ 2.5m / s². 2 Sperling comfort index ≤ 2.5.

[0084] The mathematical models for the transition curves to be selected are as follows:

[0085] Mathematical model of a cubic parabola:

[0086] (1)

[0087] Mathematical model of a quintic parabola:

[0088] (2)

[0089] Mathematical model of a seventh parabola:

[0090] (3)

[0091] Half-wave sine mathematical model:

[0092] (4)

[0093] A wave of sinusoidal mathematical models:

[0094] (5)

[0095] Seventh-degree quaternion mathematical model:

[0096] (6)

[0097] In equations (1) to (6), l0 is the length of the transition curve, R0 is the radius of the circular curve, and x and y are the coordinates in the local coordinate system of the mathematical model of the transition curve.

[0098] The mathematical model of the transition curve can have different polynomials. The above are just some common expressions, but are not limited to the expressions mentioned above.

[0099] Q3. Optimize longitudinal profile parameters l0

[0100] The longitudinal profile after adding the transition curve was determined by Q1 and Q2. It is also necessary to meet the requirements of minimum slope length and that the vertical curve should not coincide with the horizontal transition curve.

[0101] According to design specifications, the slope length L should meet the following requirements:

[0102] (7)

[0103] In the formula, K BP1 and K BP2 Let R0 be the horizontal distance between two adjacent slope change points, and Δi be the radius of the circular curve. max denoted as the maximum gradient difference (‰) between adjacent slope change points, and V as the design speed.

[0104] The distance S between the slope change point and the start and end points of the horizontal transition curve should be greater than the length T of the vertical curve tangent after the addition of the transition curve alignment, i.e.

[0105] (8)

[0106] In the formula K BP K is the horizontal mileage of the slope change point. Star / End Here, is the starting or ending mileage of the horizontal transition curve, T is the tangent length of the vertical curve after the addition of the transition curve alignment, p is the inner displacement, Δi is the algebraic difference between adjacent slopes, y0 is the y-coordinate of the transition curve's ending point, and β0 is the tangent angle of the transition curve's ending point. Figure 2 , Figure 3 As shown.

[0107] For a longitudinal profile of a railway line that meets the above requirements (l0 is usually taken as a whole 10m), high-speed railway dynamic detection filtering or train dynamics models are used to simulate high and low long-wave irregularities. The optimal longitudinal profile design alignment is determined by selecting the line that meets the actual engineering conditions, with the minimum amplitude of high and low long-wave irregularities and / or the optimal smoothness and / or the optimal train dynamics indicators, thus enabling the addition of transition curves to the longitudinal profile of newly built high-speed railway lines. The actual engineering conditions include: measurement technical conditions, which refer to the accuracy indicators achievable by using measuring equipment to measure the actual elevation of the longitudinal profile of the line; when the track structure of the line is ballasted track, the actual engineering conditions also include the longitudinal elevation accuracy of the tamping machine and the maximum track lifting limit; when the track structure of the line is ballastless track, the actual engineering conditions also include the sleeper fastener pad grade difference and its remaining adjustable amount.

[0108] For high-speed railway operating lines:

[0109] By modifying the track maintenance log and performing track fine-tuning or tamping operations, vertical adjustments are made to the track to add transition curves at both ends of the vertical curve in the longitudinal profile. The main steps of the implementation plan are as follows:

[0110] The specific details of each step are as follows:

[0111] S1. Measure the actual elevation H of the track. meas (K)

[0112] The actual elevation H of the longitudinal profile plane mileage K of the line is measured by measuring instruments or equipment at specific intervals or continuously. meas (K).

[0113] S2, Fitted longitudinal section parameters

[0114] The actual longitudinal profile of an operational line often does not perfectly match the recorded parameters, necessitating a refit of the longitudinal profile parameters, including the elevation H at slope change points. BP Slope i‰, slope length, and radius R0 of the circular curve.

[0115] S3. Select the initial transition curve type.

[0116] Combining the longitudinal profile parameters obtained from S2 with the selected transition curve type, its length, and the radius of the circular curve, the initial transition curve type is obtained by verifying through high-speed railway dynamic detection filtering (filter cutoff wavelength ≥120m) and / or dynamic testing. The transition curve type with the minimum amplitude of track elevation and low long-wave irregularities and / or the optimal smoothness is obtained as the initial transition curve type. The main design indicators of high-speed railway dynamic detection filtering and train dynamic testing are the same as those of newly built high-speed railway lines. The selected transition curve type is the same as that of newly built high-speed railway lines.

[0117] S4. Calculate the vertical adjustment amount v(K) of the track after adding the transition curve.

[0118] After adding the transition curve, the first step is to calculate the track design elevation H. desi (K). The design elevation of the track includes three parts: the design elevation of the front and rear slopes, the design elevation of the circular curve, and the design elevation of the first and second transition curves.

[0119] Design elevation of the front and rear slope sections of S4.1

[0120] like Figure 3 As shown, assume the horizontal mileage and elevation of the slope change point are (K) BP H BP The design elevation for any mileage K on the slope is calculated as follows:

[0121] (9)

[0122] Design elevation of S4.2 circular curve

[0123] like Figure 3 As shown, the design elevation of any mileage K on the circular curve is calculated as follows:

[0124] (10)

[0125] In the formula, T is the length of the vertical curve tangent after adding the transition curve, p is the inner displacement, R0 is the radius of the circular curve, and H is the radius of the circular curve. desi In formula (K), "±" is used for concave vertical curves and "−" is used for convex vertical curves.

[0126] Design elevations of the first and second transition curves in S4.3

[0127] Taking the cubic parabola curve as an example, the calculation process for the design elevation of the transition curve is derived. The derivation process is similar for other types of transition curves.

[0128] The starting point of the first transition curve, i.e., the mileage K of point ZH. ZH and design elevation H ZH for:

[0129] (11)

[0130] The endpoint of the second transition curve, i.e., the mileage K at point HZ. HZ and design elevation H HZ for:

[0131] (12)

[0132] In the formula, K BP and H BP These represent the horizontal mileage and elevation of the slope change point, respectively, and T is the length of the vertical curve tangent in the longitudinal profile after the addition of the transition curve alignment.

[0133] by Figure 4 Taking this as an example, calculate the mileage and elevation of any point on the first transition curve. Using the starting point ZH as the origin, the tangent line through the starting point is the x-axis, the direction of the transition curve's growth is the positive direction, the y-axis is determined perpendicular to the x-axis through the starting point, and the direction of the transition curve's curvature is the positive direction of the y-axis; this forms the local coordinate system x-ZH-y for the first transition curve. Point P(x,y) is any point on the first transition curve. Draw a perpendicular line from point P to the x-axis, intersecting at point B. Draw a vertical line from point B, intersecting the horizontal lines passing through points P and ZH at points A and C respectively. Then:

[0134] In triangles C-ZH-B and PAB there are

[0135] (13)

[0136] From the above formula, the lengths of ZH-C, BC, AB, and AP can be determined, and the horizontal mileage K of point P on the first transition curve can be calculated. P and elevation H P Determined by the following formula

[0137] (14)

[0138] Taking into account the curvature of the first transition curve, the following can be obtained: mileage K and design elevation H of the first transition curve. desi (K) is calculated using the following formula:

[0139] (15)

[0140] In the formula, x and y are the coordinates in the local coordinate system of the mathematical model of the transition curve, and K and H are... desi The second term of (K) is a fraction with "±", concave vertical curves take "+", and convex vertical curves take "−".

[0141] Taking the starting point HZ as the origin, the tangent line through the starting point as the x-axis, the direction of the transition curve's growth as the positive direction, and the perpendicular x-axis through the starting point as the y-axis, with the direction of the transition curve's curvature as the positive direction of the y-axis, we have the local coordinate system x-HZ-y for the second transition curve. Similarly, by simplification, we can obtain any mileage K and design elevation H of the second transition curve. desi (K) is calculated using the following formula:

[0142] (16)

[0143] In the formula, x and y are the coordinates in the local coordinate system of the mathematical model of the transition curve, and K and H are... desi The second term of (K) is a fraction with "±", concave vertical curves take "+", and convex vertical curves take "−".

[0144] S4.4: Track Vertical Adjustment Model

[0145] After adding transition curves at the beginning and end of the vertical curve in the longitudinal profile, the vertical adjustment amount v(K) of the track at the horizontal mileage K (usually the horizontal mileage at each sleeper) can be calculated by the track vertical adjustment amount model, which is the horizontal mileage K and the elevation H of the gradient change point. BP Nonlinear functions of the radius R0 of the circular curve and the length l0 of the transition curve.

[0146] (17)

[0147] In the formula, K represents the horizontal mileage, and H... desi (K) represents the design elevation after the addition of the transition curve, H meas (K) represents the actual elevation. H BPR' represents the elevation of the slope change point, R' represents the radius of the circular curve before the addition of the transition curve, and l0 represents the length of the added transition curve. Here, ΔR represents the change in radius: ΔR=0 indicates that the radius of the circular curve remains unchanged after the addition of the transition curve; ΔR>0 indicates that the radius of the circular curve increases after the addition of the transition curve; ΔR<0 indicates that the radius of the circular curve decreases after the addition of the transition curve.

[0148] S5. Determine the actual adjustable values ​​χ(K) and ζ(K) of the track.

[0149] Due to limitations in the actual adjustable range of the track, the v(K) obtained in S4 cannot usually be directly applied to track fine-tuning or tamping operations. For ballastless tracks, the actual vertical adjustability of each sleeper fastener is limited, while for ballasted tracks, track can only be raised, not lowered. Therefore, on-site verification is required to determine the actual adjustable ranges χ(K) and ζ(K) of the track.

[0150] For ballastless track, χ(K) is the actual maximum amount of sleeper fastener that can be lowered to the track at horizontal mileage K, and ζ(K) is the actual maximum amount of sleeper fastener that can be lifted to the track at horizontal mileage K. For ballasted track, χ(K) is the actual minimum amount of track that can be lifted (usually 0), and ζ(K) is the actual maximum amount of track that can be lifted.

[0151] S6. Optimize longitudinal profile parameters

[0152] The vertical track adjustment calculated in S4 is checked to determine if it meets the requirements of the actual adjustable amount in S5. Additionally, it is necessary to check whether the minimum gradient length and the distance between the gradient change point and the start and end points of the horizontal transition curve meet the design specifications after adding the transition curve. If not, the selected transition curve is filtered and / or dynamically tested using preset high-speed railway dynamic detection filtering and / or train dynamics indicators, and the elevation H of the gradient change point is checked. BP Optimize and / or adjust the radius R0 of the circular curve and / or the length l0 of the transition curve, and then repeat step S4 until all relevant requirements are met.

[0153] S6. Optimize longitudinal profile parameters

[0154] The adjustment amount calculated according to formula (18) is constrained by the actual adjustable amount of the track, and the constraint conditions are as follows:

[0155] (18)

[0156] Furthermore, according to design specifications, the minimum slope length l min Should meet

[0157] (19)

[0158] In the formula, R0 is the radius of the circular curve, and Δi maxLet S be the maximum algebraic difference (‰) between adjacent slope segments, and V be the design speed. The distance S between the slope change point and the start and end points of the horizontal transition curve should be greater than the length T of the vertical curve tangent after the addition of the transition curve alignment.

[0159] (20)

[0160] In the formula, K BP K is the horizontal mileage of the slope change point. Star / End The starting or ending mileage of the horizontal transition curve is T, where T is the length of the vertical curve tangent after the addition of the transition curve alignment.

[0161] In summary, for high-speed railway lines in operation, with transition curves added at both ends of the vertical curve in the longitudinal profile, the track vertical adjustment model and constraints can be described as follows:

[0162] (twenty one)

[0163] As can be seen from equation (21), at the same mileage, different parameters H BP R0 and l0 have different track adjustment amounts. Therefore, it is necessary to optimize and adjust the longitudinal profile parameters according to the constraints of equation (21). This step is to ensure that the vertical adjustment amount of the track meets the constraints of the track adjustable amount, so that it can be applied to the track fine adjustment or tamping operation, making it practically feasible to add transition curves at both ends of the vertical curve of the longitudinal profile of the high-speed railway. Specifically, according to the constraints, all transition curve profiles that meet the constraints are calculated, and through the preset high-speed railway dynamic detection filtering and / or train dynamics index, the vertical curves after adding all transition curve profiles are filtered and / or tested for train dynamics. The optimized parameters corresponding to the longitudinal profile vertical curve that meets the actual engineering conditions with the minimum amplitude of high and low long wave irregularities and / or the optimal smoothness or the optimal dynamic index are selected as the optimal solution of the longitudinal profile parameters (mathematical model of transition curve, length of transition curve and radius of circular curve) of the longitudinal profile vertical curve after adding the optimal transition curve profile.

[0164] S7: Perform track fine-tuning or tamping operations

[0165] Based on the optimized longitudinal profile parameters, the vertical adjustment amount of the track is calculated. For ballastless track, adjustment schemes are output for each sleeper to guide the track fine-tuning operation. For ballasted track, adjustment schemes in *.Ver format are generated at specific intervals (usually 1m or 2m) and input into the tamping machine's Automatic Leit Computer (ALC) for the tamping machine to perform the track fine-tamping operation.

[0166] According to the above technical solution, it is possible to add transition curves at both ends of the vertical curve in the longitudinal profile of high-speed railway, thereby solving the problems of sudden vertical acceleration of the vehicle body at the beginning and end of the vertical curve, strong impact and vibration of the vehicle, and unevenness of high and low long waves in the dynamic detection of high-speed railway.

[0167] This invention discloses an optimized method for dynamically detecting long-wave irregularities in the vertical curves of high-speed railway tracks. This method is achieved by adding transition curves at both ends of the vertical curve in the longitudinal profile, hereinafter referred to as the vertical curve with added transition curves. The vertical curve with added transition curves consists of five basic alignment types: a front slope section, a first transition curve, a circular curve, a second transition curve, and a rear slope section. The connection point between the front slope section and the first transition curve is the straight-to-transition (ZH) point; the connection point between the first transition curve and the circular curve is the transition-to-circular (HY) point; the connection point between the circular curve and the second transition curve is the circular-to-transition (YH) point; and the connection point between the second transition curve and the rear slope section is the transition-to-straight (HZ) point. This invention can solve the problems of abrupt changes in vertical acceleration at the beginning and end of the vertical curve in the longitudinal profile of high-speed railway tracks and long-wave irregularities at varying elevations, and further improves the vertical smoothness of the track.

[0168] For newly constructed high-speed railway lines, during the route selection and design phase, the connection between the preceding and following gradient sections is designed using transition curves, circular curves, and other transition curve methods, according to the line design requirements, and this is applied during construction. For lines with different design speeds, the minimum circular curve radius, minimum gradient length, and distance between the gradient change point and the start and end points of the horizontal transition curve in the longitudinal profile should meet the requirements of the high-speed railway design specifications. ① Minimum circular curve radius: 20000m (250km / h), 25000m (300~350km / h). ② Minimum gradient length: 800m (200~250 km / h), 900m (300~350 km / h). ③ The distance between the gradient change point and the start and end points of the horizontal transition curve is greater than the tangent length of the vertical curve after the addition of the transition curve. Assume that the longitudinal and horizontal profile design of a newly constructed high-speed railway with a design speed of 350km / h is as follows... Figure 6 As shown, the implementation process of adding a transition curve to the longitudinal section is given below according to the technical solution.

[0169] Q1. Determine longitudinal profile parameters

[0170] like Figure 6 As shown in the figure, there are three gradient change points in the section from K276 to K280. Taking the second gradient change point as an example, the specific process of adding a transition curve is illustrated. As can be seen from the figure, the elevation of the second gradient change point is H. BP =29.576m, with a front slope of i‰=10.3‰ and a rear slope of i‰=6‰. The radius of the circular curve is designed to be R0=25000m.

[0171] Q2. Determine the initial transition curve shape.

[0172] Based on the longitudinal profile parameters obtained from Q1, a cubic parabolic curve and a single-wave sinusoidal curve are selected as examples. Using a 120m high-low long-wave filtering model for dynamic testing of high-speed railways, the waveforms of track high-low long-wave irregularities are verified under transition curve lengths of 150m, 200m, 250m, and 300m, such as... Figure 7 As shown in the figure. The calculation results show that when the transition curve length is less than 200m, the amplitude of the long-wave irregularities in the track obtained by adding a cubic parabolic shape is smaller; when the transition curve length is greater than 200m, the wavelength of the irregularities in the track obtained by adding a single-wave sinusoidal parabolic shape is longer. Assuming a cubic parabolic shape is chosen as the initial transition curve shape for the longitudinal profile, explain the steps for adding the transition curve shape.

[0173] Q3. Optimize longitudinal profile parameters l0

[0174] The vertical curve needs to meet the requirements of minimum slope length and that the vertical curve should not coincide with the horizontal transition curve. According to formula (7), the minimum slope length can be calculated to be 140m, the front slope length is 1480m, and the back slope length is 2324m, all of which meet the requirements.

[0175] Next, verify the requirement that the vertical curve coincides with the horizontal transition curve. Figure 6 The gradient change point is at kilometer marker K277+499, located on a horizontal circular curve. According to formula (8), the distances S between the gradient change point and the start and end points of the horizontal transition curve are 301m and 341m, respectively. Therefore, the length T of the vertical curve tangent after adding the transition curve should be less than 301m. According to formulas (8) and (9), the length of the added transition curve should be less than 194m.

[0176] Depend on Figure 7 The simulated uneven waveform of the track shows that the longer the transition curve, the better the smoothness of the vertical curve with varying elevations at the beginning and end. Therefore, the optimal longitudinal profile design line can have a transition curve length l0 of 190m. Figure 8 The paper presents a comparison of the unevenness of the long waves at the beginning and end of the vertical curve before and after the addition of the transition curve.

[0177] from Figure 8 It can be seen that at the vertical curve of the longitudinal profile from K277 to K278, without a transition curve, the maximum amplitude of the long-wave irregularity of the track elevation is 3 mm. When a cubic parabolic transition curve with a length of 190 m is added at both ends of the vertical curve of the longitudinal profile, the maximum amplitude of the long-wave irregularity of the track elevation is reduced to 0.6 mm, a reduction of 80%. Therefore, adding transition curves at both ends of the vertical curve of the longitudinal profile can effectively reduce the long-wave irregularity of the track elevation of high-speed railways.

[0178] Taking ballastless track in high-speed railways during operation as an example, this study verifies the feasibility of adding transition curves at both ends of vertical curves, and their effect on reducing the unevenness of dynamic detection of long-wave irregularities. The difference with ballasted track is that it can only be used for starting the track but not for ending it, but the calculation approach is basically the same.

[0179] Taking the longitudinal profile of a high-speed railway operating at 350 km / h as an example, the feasibility of adding cubic parabolic transition curves at both ends of the vertical curve in the longitudinal profile is verified. Figure 9 The selected concave and convex vertical curve segments are shown, and the design parameters of the longitudinal profile are marked on the figure. The mileage ranges of the nearest horizontal transition curves to the beginning and end of the concave vertical curves are: K2368+650~K2369+320, K2377+613~K2378+283, respectively. The mileage ranges of the nearest horizontal transition curves to the beginning and end of the convex vertical curves are: K2350+414~K2351+084, K2358+075~2358+745, respectively.

[0180] S1. Measure the actual elevation H of the track. meas (K).

[0181] Measure the actual elevation H of the longitudinal profile reference rail meas (K), such as Figure 10 As shown in the figure. The upper figure shows the measured elevation of the concave vertical curve segment, and the lower figure shows the measured elevation of the convex vertical curve segment. The horizontal axis represents the horizontal mileage (m), and the left vertical axis represents the measured elevation (m).

[0182] S2, Fitting longitudinal section parameters.

[0183] The longitudinal section was fitted using least squares, and the fitting deviation was as follows: Figure 10 As shown in Table 1, the fitted longitudinal profile results are as follows:

[0184] Table 1

[0185]

[0186] The fitting results show that the longitudinal profile parameters are not significantly different from the design parameters of the ledger.

[0187] S3. Select the optimal easing curve.

[0188] Using a pre-set dynamic detection filter for high-speed railways, the filter processing and verification of the added cubic parabolic curve and the single-wave sinusoidal transition curve are performed. The relationship between the peak value and standard deviation of the unevenness and the increase in transition length is statistically analyzed. Figure 11As shown in the figure. Filtering verification shows that, under the same conditions, the longer the transition curve, the smaller the peak value and standard deviation of the unevenness, and the cubic parabola is superior to the single-wave sine curve. When the radius of the circular curve is 25000m and the length of the transition curve exceeds 100m, the peak value of the unevenness is less than 1mm, and the standard deviation is less than 0.4. Therefore, the cubic parabola is selected as the optimal mathematical model for the transition curve, and the transition length is set to be greater than 100m.

[0189] S4. Calculate the vertical adjustment amount of the track.

[0190] For concave vertical curves, according to the S2 fitting of longitudinal profile parameters, H BP =24.157m, the radius is rounded to R0=25000m, and l0=120m is set. Substitute these values ​​into equations (9), (10) and (15) and (16) respectively to calculate the design elevation H of the front and rear slope sections, the circular curve and the transition curve. desi (K), and then the vertical adjustment amount of the track can be calculated according to formula (17).

[0191] For a convex vertical curve, according to the S2 fitting of the longitudinal profile parameters, H BP =88.23m, the radius is rounded to R0=25000m, and l0=120m is set. Substitute these values ​​into equation (17) to calculate the vertical adjustment of the track, such as Figure 12 As shown.

[0192] Definition: Track vertical adjustment amount = Design elevation after adding transition curve - Actual track elevation, + value indicates track start, - value indicates track drop (ballastless).

[0193] S5, Actual adjustable range of the track.

[0194] Taking the common WJ-7 or WJ-8 type fasteners as an example, their vertical adjustment range is -4 to +26 mm. Since the actual vertical adjustment range of each sleeper fastener is not statistically analyzed, the theoretical adjustment range of the fasteners, -4 to +26 mm, is used in the example to replace the actual adjustment range, i.e., χ(K) = -4 mm, ζ(K) = 26 mm.

[0195] When the radius remains constant and a transition curve with a length of 120m is added, for a concave vertical curve, the maximum track lifting amount is 26.5mm > ζ(K); for a convex vertical curve, the maximum track lowering amount is -18.7mm < χ(K). Therefore, neither meets the requirements for the adjustable amount of the sleeper fasteners, and further optimization of the longitudinal profile parameters is needed.

[0196] S6. Optimize longitudinal profile parameters.

[0197] As shown in S4, keeping the radius of the circular curve unchanged (the same as in the design plan), after adding a transition curve with a length of 120, the vertical adjustment of the track for both the concave and convex vertical curves exceeds the actual adjustable range of the fasteners, making fine-tuning impossible on-site. Next, the longitudinal profile parameters will be optimized by reducing the radius of the circular curve or increasing the length of the transition curve. Repeat S4 to calculate the optimized vertical adjustment of the track, such as... Figure 12 As shown, the calculation is performed using a preset high-speed railway dynamic detection filter, such as... Figure 13 As shown.

[0198] After optimizing the radius and transition length, the maximum track drop and maximum track rise of the concave and convex vertical curves are -2.8mm and 14.2mm, and -3.8mm and 25.4mm, respectively. Therefore, both meet the requirements for adjustable sleeper fasteners. Dynamic testing over a 120m long wave shows that without the transition curve, the peak value of the unevenness is nearly 2.5mm with a standard deviation of 1mm. After adding and optimizing the transition curve, the peak value of the unevenness is less than 1mm with a standard deviation of less than 0.4mm, demonstrating a significant reduction in unevenness.

[0199] According to design specifications, for high-speed railway lines with a design speed of 300-350 km / h, the minimum longitudinal slope length should be greater than 900 m. It is necessary to check whether the slope length after the addition of a transition curve meets the requirements. Table 2 shows the corresponding front and rear slope lengths for concave and convex vertical curves.

[0200] Table 2

[0201]

[0202] As shown in Table 2, the slope lengths of the longitudinal profiles all meet the specifications after the addition of the transition curves. Furthermore, according to the specifications, vertical curves should not overlap with horizontal transition curves. The following judgment is made using the tangent length of the vertical curve; that is, the distance S between the slope change point and the start or end point of the horizontal transition curve should be greater than the tangent length T of the vertical curve after the addition of the transition curve. The calculation of the tangent length of the vertical curve is as follows:

[0203]

[0204] The distances between the change-of-slope point and the start and end points of the horizontal transition curve are shown in Table 3:

[0205] Table 3

[0206]

[0207] According to the results in Table 3, after adding the transition curve, the distance between the slope change point and the starting or ending point of the horizontal transition curve is greater than the length of the tangent of the vertical curve after adding the transition curve. That is, the vertical curve does not overlap with the horizontal transition curve, which meets the design specifications.

[0208] S7. Perform track fine-tuning operations.

[0209] By adding transition curves based on the optimized radius and gradient of S6, not only are the vertical adjustments of the track within the adjustable range, but the setting of the vertical curves also meets the specifications, allowing for track fine-tuning operations. Figure 14 Comparison of long-wave irregularities in track height before and after adding the transition curve according to S6.

[0210] The comparison reveals that adding transition curves effectively resolves the long-wave irregularities at the beginning and end of the vertical curves in the longitudinal profile, and significantly reduces the peak value of long-wave irregularities in track elevation. Therefore, the method provided by this invention can effectively reduce long-wave irregularities in elevation at the beginning and end of the vertical curves in the longitudinal profile of high-speed railway tracks.

[0211] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for optimizing the dynamic long-wave irregularities of vertical curves in high-speed railways, characterized in that: include: Obtain the longitudinal profile type of the line, the longitudinal profile parameters corresponding to the longitudinal profile type of the line, and the transition curve to be selected. The longitudinal profile type of the line is either a newly built line longitudinal profile or an operating line longitudinal profile. Based on the preset dynamic detection filtering and / or train dynamics indicators for high-speed railways, the vertical curves of the longitudinal profile of the line after adding each transition curve are filtered and / or dynamically tested respectively. Based on the results of each filtering and / or test, the vertical curve of the longitudinal profile of the line that satisfies the minimum amplitude of high and low long wave irregularities and / or the optimal smoothness under actual engineering conditions is selected as the initial vertical curve of the longitudinal profile of the line. The longitudinal profile parameters of the initial vertical curve of the longitudinal profile of the line are used as the parameters to be optimized. Select preset constraint conditions according to the type of longitudinal profile of the line. When the type of longitudinal profile of the line is a newly built line, the constraint conditions include minimum slope length constraint and constraint that the vertical curve does not coincide with the horizontal transition curve. When the type of longitudinal profile of the line is an operating line, the constraint conditions include track vertical adjustability or track take-off and landing volume constraint, minimum slope length constraint and constraint that the vertical curve does not coincide with the horizontal transition curve. Based on the parameters to be optimized and the initial longitudinal profile vertical curve, solve for the longitudinal profile vertical curves corresponding to all longitudinal profile parameters that satisfy the constraints. Through preset high-speed railway dynamic detection filtering and / or train dynamics indices, filter and / or test the longitudinal profile vertical curves corresponding to all parameters that satisfy the constraints one by one. Select the longitudinal profile parameter that satisfies one or more of the following conditions under actual engineering conditions: minimum amplitude of high and low long wave irregularities, optimal smoothness, and optimal train dynamics indices as the optimal solution. The vertical adjustment amount of the track is calculated according to the optimal solution. For ballastless track, the adjustment plan is output for each sleeper according to the vertical adjustment amount of the track. For ballasted track, the adjustment plan is generated at a specific interval according to the vertical adjustment amount of the track. Based on preset dynamic detection filtering and / or train dynamics indicators for high-speed railways, the vertical curves of the longitudinal profile of the line after the addition of each transition curve are subjected to filtering processing and / or dynamic testing, including: Based on the selected transition curve, the longitudinal profile type of the line, and the longitudinal profile type of the line, calculate the mathematical model of each transition curve and its length and radius of the circular curve. The mathematical model of the transition curve includes a cubic parabola mathematical model, a quintic parabola mathematical model, a seventh parabola mathematical model, a half-wave sine mathematical model, a one-wave sine mathematical model, and a seventh-order quadrilateral mathematical model. Calculate the mathematical model of each transition curve, its length, and the radius of the circular curve, and add the transition curve to the vertical curve of the longitudinal profile of the line to obtain the vertical curve of the longitudinal profile of the line after adding the transition curve; By using preset high-speed railway dynamic detection filtering indicators and / or train dynamics indicators, the vertical curves of the longitudinal profile of the line after the addition of each transition curve are filtered and / or dynamically tested respectively. The mathematical model for the transition curve includes: Mathematical model of a cubic parabola: ， Mathematical model of a quintic parabola: ， Mathematical model of a seventh parabola: ， Half-wave sine mathematical model: ， A wave of sinusoidal mathematical models: ， Seventh-degree quaternion mathematical model: ， In the formula, l0 is the length of the transition curve, R0 is the radius of the circular curve, x and y are the coordinates in the local coordinate system of the mathematical model of the transition curve. The local coordinate system takes the starting point of the transition curve as the origin, the tangent line through the starting point as the x-axis, the growth direction of the transition curve as the positive direction, the perpendicular x-axis through the starting point as the y-axis, and the bending direction of the transition curve as the positive direction of the y-axis. In the constraints: The minimum slope length constraint is: ， The constraint that the vertical curve does not coincide with the planar transition curve is: ， The vertical adjustability constraint of the track is: ， Where L represents the length of the slope, K BP1 and K BP2 Let R0 be the horizontal mileage of two adjacent slope change points, R0 be the radius of the circular curve, and Δi be the algebraic difference (‰) between adjacent slopes. max The maximum absolute value of Δi is given, V is the design speed, and K is the maximum value of Δi. BP K is the horizontal mileage of the slope change point. Star / End Here, is the starting or ending mileage of the horizontal transition curve, T is the tangent length after the addition of the transition curve alignment, p is the internal displacement, y0 is the y-coordinate of the transition curve's ending point, β0 is the tangent angle of the transition curve's ending point, v(K) represents the track's vertical deviation, χ(K) and ζ(K) represent the lower and upper limits of the actual adjustable amount of the track, respectively, and H... desi (K) represents the design elevation of the vertical curve of the longitudinal profile of the operating line after the addition of the transition curve alignment; H meas (K) represents the actual elevation of the vertical curve of the longitudinal profile of the operating line, and the track vertical deviation v(K) is related to the mileage K and the elevation H of the gradient change point. BP The design elevation is a nonlinear function of the radius R0 of the circular curve and the length l0 of the transition curve. The design elevation includes: the design elevation of the front and back slopes, the design elevation of the circular curve, the design elevation of the first transition curve, and the design elevation of the second transition curve. The first transition curve is the transition curve between the front slope and the circular curve, and the second transition curve is the transition curve between the circular curve and the back slope. When the design elevation is the same as the design elevation of the front and rear slope sections, the design elevation H desi The formula for calculating (K) is: ， In the formula K BP and H BP Let K be the horizontal mileage and elevation of the slope change point, K be the mileage of any point on the slope segment, and i be the slope of the slope segment corresponding to mileage K. ZH K represents the distance between the straight and gentle curve points on a vertical curve. HZ Indicates the mileage of the transition point between vertical and straight sections; When the design elevation is the same as the design elevation of the circular curve, the design elevation H desi The formula for calculating (K) is: ， In the formula, p is the inner displacement, R0 is the radius of the circular curve, and H... desi (K) The first term of the fraction is "±", concave vertical curves are "+", and convex vertical curves are "−", K HY K represents the mileage of the transition point of the vertical curve. YH Indicates the mileage of the transition point of the vertical curve; When the design elevation is the design elevation of the transition curve, any mileage K and design elevation H desi (K) is calculated using the following formula: ， In the formula, T is the length of the vertical curve tangent after the addition of the transition curve, i is the slope at the starting point of the transition curve (in‰), and K and H... desi (K) takes the plus sign "±" for the first fractional term, and the minus sign "−" for the second transition curve; K and H desi The second term of (K) is a fraction with "±", concave vertical curves take "+", and convex vertical curves take "−".

2. The method for optimizing dynamic long-wave irregularities of vertical curves in high-speed railways according to claim 1, characterized in that: Obtaining the longitudinal profile parameters corresponding to the longitudinal profile type of the line includes: When the longitudinal profile type of the line is a newly built line longitudinal profile, the longitudinal profile design parameters obtained according to the high-speed railway design specifications are used as the longitudinal profile parameters. The longitudinal profile design parameters include the elevation of the slope change point, the slope length, and the radius of the circular curve. When the longitudinal profile type of the line is an operational line longitudinal profile, the actual elevation of the longitudinal profile is precisely measured, and the longitudinal profile fitting parameters are obtained based on the actual elevation of the longitudinal profile as longitudinal profile parameters. The longitudinal profile fitting parameters include the elevation of the slope change point, the slope length, and the radius of the circular curve.

3. The method for optimizing dynamic long-wave irregularities of vertical curves in high-speed railways according to claim 1, characterized in that: The high-speed railway dynamic detection filtering includes: passband cutoff wavelength ≥120m, maximum passband attenuation -3dB, and stopband minimum slope of 24dB / octave. The train dynamics indicators include: derailment coefficient ≤0.8, wheel load reduction rate ≤0.6, and vertical vibration acceleration of the car body ≤2.5m / s². 2 Sperling comfort index ≤ 2.

5.

4. The method for optimizing dynamic long-wave irregularities of vertical curves in high-speed railways according to claim 3, characterized in that: The passband cutoff wavelengths include 120m, 150m, 200m and >200m.

5. The method for optimizing dynamic long-wave irregularities of vertical curves in high-speed railways according to claim 1, characterized in that: The actual engineering conditions include: Measurement technical conditions, which refer to the accuracy indicators that can be achieved by using measurement equipment to measure the actual elevation of the longitudinal profile of the line; Construction technical conditions, when the track structure of the line is ballasted track, include but are not limited to the longitudinal height and low operation accuracy of the tamping machine and the maximum track lifting volume limit; when the track structure of the line is ballastless track, the construction technical conditions include but are not limited to the sleeper fastener pad grade difference and its remaining adjustable amount.

Images