High-speed railway vertical curve dynamic long wave irregularity optimization method

Abstract

The invention discloses a high-speed railway vertical curve dynamic long wave irregularity optimization method, which comprises the following steps: acquiring a line vertical section of a new line or an operation line and parameters thereof, and dynamically detecting filtering and / or driving dynamics indexes according to a preset high-speed railway, determining an easement curve mathematical model corresponding to the initial easement curve line type and the length and the circular curve radius thereof, adding the initial easement curve line type to the head and the tail of the line vertical section circular curve, constructing constraint conditions according to the vertical section characteristics of the new line or the operation line, and solving all vertical section vertical curve optimization parameters meeting the constraint conditions; and designing and constructing according to actual engineering conditions. The method is wide in 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 the tail of the longitudinal section circular curve, can weaken the irregularity of long waves of 120 m and above in dynamic detection of the head and the tail of the high-speed railway circular curve, and effectively improves the dynamic vertical smoothness of the high-speed railway.

Description

Technical Field

[0001] The present invention relates to the technical field of high-speed railway line selection design and operation and maintenance, and in particular to a method for optimizing dynamic long-wave irregularities of a vertical curve of a high-speed railway. Background Art

[0002] As trains run at higher and higher speeds, researchers have begun to study the optimization of vertical curves in longitudinal sections. In the design stage of new lines, patent document CN113742812A discloses the use of half-wave sinusoidal curves and quartic curves between adjacent ramps to eliminate the vertical impact between wheels and rails at the connection point. Patent document CN109165427A discloses that for high-speed railways in operation, multi-slope fitting and radius adjustment are proposed to optimize the longitudinal section; in the paper "Optimization of the Smoothness of Vertical Curves of High-speed Railways and Engineering Applications", it is disclosed that the smoothness of the longitudinal section is improved by expanding the radius of the circular curve.

[0003] However, the above-mentioned prior art has the following defects: Patent document CN113742812A is only applicable to the longitudinal section design of newly built lines, not to operating lines; for the high-speed railways already in operation, the multi-slope fitting of patent document CN109165427A cannot solve the problem of uneven long waves at the beginning and end of the vertical curve; the method of expanding the radius of the circular curve cannot eliminate the problem of sudden vertical velocity changes, and considering the difficulty of on-site construction and maintenance, the incremental amount of the circular curve radius is very limited, especially for convex slope change points, which are limited by the amount of track that can be dropped, and expanding the radius is even more unfeasible. In particular, the current operating line's achievements in improving the unevenness of the vertical curves at the head and tail are mainly technical summaries or experience summaries of individual engineering tests. The changed longitudinal section line shape has not undergone high-speed railway dynamic detection filtering inspection or vehicle driving dynamics test, nor the static 300m chord height index inspection. It only reduces the high and low long wave amplitudes of the track in a specific test section to below the acceptance index after dynamic inspection by the high-speed railway comprehensive inspection vehicle. The goal is to avoid scoring, that is, no first-level deduction. Not only has the dynamic and static unevenness of the longitudinal section of the line not been thoroughly rectified, but it has also caused distortion of the static geometry of the track and the line shape of the high-speed railway engineering ledger, which will cause difficulties for the subsequent scientific maintenance and management of the high-speed railway engineering department.

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

[0005] The present invention proposes a method for optimizing the dynamic long-wave irregularity of a high-speed railway vertical curve, so as to solve the problem that the existing high-speed railway longitudinal section vertical curve design and operation and maintenance method cannot be applied to both newly built lines and operating lines at the same time, resulting in a sudden change in the vertical acceleration of the high-speed railway dynamic detection at the beginning and end of the longitudinal section vertical curve, causing long-wave irregularity of more than 120m in the track height.

[0006] The present invention achieves the above-mentioned purpose through the following technical solutions:

[0007] The present invention provides a method for optimizing dynamic long-wave irregularity of a high-speed railway vertical curve, comprising:

[0008] Obtaining a line profile type, profile parameters corresponding to the line profile type, and a transition curve to be selected, wherein the line profile type is a newly built line profile or an operating line profile;

[0009] According to the preset high-speed railway dynamic detection filter and / or driving dynamics index, the vertical curves of the longitudinal section of the line after adding each transition curve are respectively subjected to filtering processing and / or dynamic testing, and the vertical curves of the longitudinal section of the line with the minimum amplitude of high and low long wave irregularities and / or the best smoothness under actual engineering conditions are selected as the initial vertical curves of the longitudinal section of the line according to the results of each filtering processing and / or testing, and the longitudinal section parameters of the initial vertical curves of the longitudinal section of the line are used as the parameters to be optimized;

[0010] Selecting preset constraints according to the line profile type; when the line profile type is a newly built line profile, the constraints include a minimum slope section length constraint and a vertical curve that does not coincide with a plane transition curve; when the line profile type is an operating line profile, the constraints include a track vertical adjustable amount or track start amount constraint, a minimum slope section length constraint, and a vertical curve that does not coincide with a plane transition curve;

[0011] According to the parameters to be optimized and the vertical curve of the initial line longitudinal section, the vertical curve of the line longitudinal section corresponding to all the longitudinal section parameters that meet the constraint conditions is solved, and the vertical curve of the line longitudinal section corresponding to all the parameters that meet the constraint conditions is filtered and / or tested for driving dynamics one by one through a preset high-speed railway dynamic detection filter and / or driving dynamics index, and the longitudinal section parameters that meet any one or more conditions of minimum amplitude of track high and low long wave irregularities, optimal smoothness and optimal driving dynamics index under actual engineering conditions are selected as the optimal solution.

[0012] Obtain the longitudinal section parameters corresponding to the line longitudinal section type, including:

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

[0014] When the line longitudinal section type is an operating line longitudinal section, the actual elevation of the line longitudinal section is precisely measured, and the longitudinal section fitting parameters are obtained according to the actual elevation fitting of the line longitudinal section as longitudinal section parameters, and the longitudinal section fitting parameters include the elevation of the slope change point, the slope section length and the circular curve radius.

[0015] According to the preset high-speed railway dynamic detection filter and / or driving dynamics index, the vertical curves of the longitudinal section of the line after adding each transition curve are filtered and / or dynamically tested, including:

[0016] Calculating the mathematical model of the transition curve corresponding to each transition curve and its length and the radius of the circular curve according to the transition curve to be selected, the line longitudinal section type, and the line longitudinal section type, wherein the mathematical model of the transition curve includes a cubic parabola mathematical model, a quintic parabola mathematical model, a septad parabola mathematical model, a half-wave sine mathematical model, a single-wave sine mathematical model, and a septad quaternary mathematical model;

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

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

[0019] The mathematical model of the relaxation curve includes:

[0020] Cubic parabola mathematical model:

[0021]

[0022] Mathematical model of quintic parabola:

[0023]

[0024] Mathematical model of the seventh parabola:

[0025]

[0026] Half-wave sine mathematical model:

[0027]

[0028] Mathematical model of a sine wave:

[0029]

[0030] Seventh-order quaternary mathematical model:

[0031]

[0032] In the formula, l 0 is the length of the transition curve, R 0 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, and the tangent through the starting point is the x-axis, the growth direction of the transition curve is the positive direction, and the y-axis is determined by passing through the starting point perpendicular to the x-axis, and the bending direction of the transition curve is the positive direction of the y-axis.

[0033] Among the constraints:

[0034] The minimum slope length constraint is:

[0035]

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

[0037]

[0038] The vertical adjustable amount of the track is constrained as follows:

[0039]

[0040] Where L represents the length of the slope, K BP1 and K BP2 is the plane mileage of two adjacent slope change points, R 0 is the radius of the circular curve, Δi is the algebraic difference (‰) between adjacent slope sections, Δi max is the maximum absolute value of Δi, V is the design speed, K BP is the horizontal mileage of the slope change point, K Star / End is the starting or ending mileage of the plane transition curve, T is the tangent length after adding the transition curve line type, p is the inward displacement, y 0 is the y coordinate of the end point of the transition curve, β 0 is the tangent angle of the end point of the transition curve, v(K) represents the vertical deviation of the track, 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 section of the operating line after adding the transition curve line type, H meas (K) represents the actual elevation of the vertical curve of the longitudinal section of the operating line. The vertical deviation of the track v(K) is the value of the mileage K and the elevation of the slope change point H. BP , Circular curve radius R 0 , the length of the transition curve l 0The design elevation comprises: the design elevations of the front and rear 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 a transition curve between the front slope section and the circular curve, and the second transition curve is a transition curve between the circular curve and the rear slope section.

[0041] When the design elevation is the design elevation of the front and rear slope sections, the design elevation H desi (K) is calculated as:

[0042]

[0043] Where K BP and H BP are the plane mileage and elevation of the slope change point, K is the mileage of any point on the slope section, i is the slope of the slope section corresponding to the mileage K, K ZH Indicates the mileage of the vertical curve straight slow point, K HZ Indicates the mileage of the vertical curve straightening point;

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

[0045]

[0046] Where p is the internal displacement, R 0 is the radius of the circular curve, H desi In the formula (K), the “±” in the concave vertical curve is “+”, and the convex vertical curve is “−”. HY Indicates the mileage of the vertical curve transition point, K YH Indicates the mileage of the vertical curve circle slow point.

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

[0048]

[0049] Where, T is the length of the vertical curve tangent of the longitudinal section after adding the transition curve line type, i is the slope at the starting point of the transition curve, unit ‰, K and H desi The first term of the fractional expression of (K) is “±”, the first transition curve is “+”, and the second transition curve is “−”; K and H desi The second term of the fraction (K) is “±”, the concave vertical curve is “+”, and the convex vertical curve is “−”.

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

[0051] Passband cut-off 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 measuring the actual elevation of the longitudinal section of the line using measurement equipment;

[0054] Technical construction conditions. When the track structure of the line is a ballasted track, the technical construction conditions also include but are not limited to the longitudinal height operation accuracy of the tamping vehicle and the maximum track lifting amount limit. When the track structure of the line is a ballastless track, the technical construction conditions also include but are not limited to the level difference of the sleeper fastener pad and its remaining adjustable amount.

[0055] The beneficial effects of the present invention are:

[0056] 1. The present invention provides a method for optimizing the dynamic long-wave unevenness of a high-speed railway vertical curve, which solves the problem that the existing high-speed railway longitudinal section vertical curve design and operation and maintenance methods cannot be simultaneously applied to newly built lines and operating lines, and the obtained track dynamic smoothness has not been tested by high-speed railway dynamic filtering and / or vehicle driving dynamics, resulting in a sudden change in the vertical acceleration of the high-speed railway dynamic detection at the beginning and end of the longitudinal section vertical curve, causing long-wave unevenness of the operating track with a height of more than 120m.

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

[0058] 3. Adding vertical curves to the longitudinal section of the transition curve not only makes the transition between the straight line and the circular curve smoother, but also can appropriately reduce the radius of the circular curve in the line selection design, increase the flexibility to adapt to the undulating terrain, reduce the project cost, and make the high-speed railway line after completion, and make the high-speed travel of trains smoother; make the long-wave smoothness of the high and low track heights of the operating line higher, and further improve the stability and comfort of passengers riding on high-speed railway trains.

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

[0060] 5. Adjust relevant parameters according to the dynamic detection filter wavelength and / or driving dynamics index and design specification requirements corresponding to conventional railways, urban rail transit and underground railways. The present invention is also applicable to the long-wave unevenness optimization of vertical curve dynamic detection of longitudinal sections of conventional railways, urban rail transit and underground railways. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 A schematic diagram of a vertical curve of a longitudinal section with a transition curve added in an embodiment of the present invention;

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

[0063] Figure 3 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 It is a diagram illustrating the calculation of plane mileage and elevation of a transition curve in an embodiment of the present invention;

[0065] Figure 5 A schematic diagram showing the comparison of vertical acceleration before and after the transition curve is added in the embodiment of the present invention;

[0066] Figure 6 Design the line type of the horizontal and vertical sections of a newly built high-speed railway in an embodiment of the present invention;

[0067] Figure 7 After adding different transition curve line types in the embodiment of the present invention, the track height and long wave are not smooth;

[0068] Figure 8 The embodiment of the present invention adds a high and low long wave comparison of the gentle curve track in the longitudinal section of the newly built high-speed railway line.

[0069] Fig. 9 9 is a schematic diagram of the concave and convex vertical curve segments selected in the embodiment of the present invention (9 (a) and 9 (b) represent the concave and convex vertical curve segments respectively);

[0070] Fig.10 10(a) and 10(b) are schematic diagrams of deviations of measured elevations and fittings of longitudinal sections in an embodiment of the present invention (10(a) and 10(b) are schematic diagrams of deviations of measured elevations and fittings of concave and convex vertical curve sections, respectively);

[0071] Fig.11 Schematic diagram of the result of calculating the type of the transition curve to be selected using the 120m high-speed railway dynamic detection filter cutoff wavelength in the embodiment of the present invention (11 (a) and 11 (b) respectively represent the peak value of the top of the irregularity and the standard deviation of the irregularity);

[0072] Fig.12Schematic 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) are schematic diagrams of the vertical adjustment amount of the track after adding a transition curve in a concave and convex vertical curve section, respectively);

[0073] Fig.13 13 (a) and (b) are schematic diagrams showing the unevenness of the vertical curve of the longitudinal section after the optimization design using the cutoff wavelength of the dynamic detection filter of a 120m high-speed railway in an embodiment of the present invention (13 (a) and 13 (b) are schematic diagrams showing the unevenness of the vertical curve of the longitudinal section after the optimization design of the concave and convex vertical curve sections, respectively);

[0074] Fig.14 Schematic diagram for comparing the long wave unevenness of the track before and after adding a transition curve in an embodiment of the present invention (14 (a) and 14 (b) are schematic diagrams for comparing the long wave unevenness of the track before and after adding a transition curve in a vertical curve section with a concave and convex longitudinal section, respectively). DETAILED DESCRIPTION

[0075] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

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

[0077] For new high-speed railway lines:

[0078] During the line selection and design stage, the front and rear slope sections are designed as transition curves, circular curves, and transition curve connections, and are applied to construction. For lines with different design speeds, the minimum circular curve radius of the line longitudinal section, the minimum slope section length, and the distance between the slope change point and the start and end point of the plane transition curve should meet the requirements of the high-speed railway design specifications. The main steps for implementing the plan are as follows:

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

[0080] Q1. Determine the longitudinal section parameters

[0081] For newly built lines, the parameters of each line longitudinal section are designed and determined according to the relevant requirements of high-speed railway design specifications, including the slope i‰ of each longitudinal section, the elevation of the slope change point H BP , slope length, circular curve radius R 0 .

[0082] Q2. Determine the initial transition curve line type

[0083] According to the results of filtering and / or dynamic testing, the transition curve with the minimum amplitude of high and low long wave irregularities and / or the best smoothness is selected. Combined with the longitudinal section parameters obtained by Q1 and the transition curve line type to be selected, the transition curve line type with the minimum amplitude of high and low long wave irregularities and / or the best smoothness is obtained through high-speed railway dynamic detection filtering (filter cutoff wavelength ≥ 120m) and / or dynamic testing, and the initial transition curve line type of the longitudinal section of each line is obtained. The main design indicators of high-speed railway dynamic detection filtering are as follows: ① passband cutoff wavelength ≥ 120m; ② passband maximum attenuation -3dB; ③ stopband minimum slope of 24dB / octave. The passband cutoff wavelength includes 120m, 150m, 200m, and longer wavelengths. The main design indicators of driving dynamics are as follows: derailment coefficient ≤ 0.8, wheel weight reduction rate ≤ 0.6, vehicle body vertical vibration acceleration ≤ 2.5m / s 2 , Sperling comfort index ≤ 2.5.

[0084] The mathematical model of the transition curve to be selected is as follows:

[0085] Cubic parabola mathematical model:

[0086] (1)

[0087] Mathematical model of quintic parabola:

[0088] (2)

[0089] Mathematical model of the seventh parabola:

[0090] (3)

[0091] Half-wave sine mathematical model:

[0092] (4)

[0093] Mathematical model of a sine wave:

[0094] (5)

[0095] Seventh-order quaternary mathematical model:

[0096] (6)

[0097] In formulas (1) to (6), 0 is the length of the transition curve, R 0 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 only provides several common expressions, but is not limited to the above expressions.

[0099] Q3. Optimize longitudinal section parameters 0

[0100] The longitudinal section after adding the transition curve is determined by Q1 and Q2, and it is also necessary to meet the requirements of the minimum length of the slope section and the vertical curve should not overlap with the plane transition curve.

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

[0102] (7)

[0103] In the formula, K BP1 and K BP2 is the plane mileage of two adjacent slope change points, R 0 is the radius of the circular curve, Δi max is the maximum slope difference between adjacent slope change points (‰), and V is the design speed.

[0104] The distance S between the slope change point and the start and end points of the plane transition curve should be greater than the length T of the tangent line of the vertical curve after adding the transition curve line type, that is,

[0105] (8)

[0106] Where K BP is the horizontal mileage of the slope change point, K Star / End is the starting or ending mileage of the plane transition curve, T is the tangent length of the vertical curve after adding the transition curve line type, p is the inward displacement, Δi is the algebraic difference between adjacent slope sections, y 0 is the y coordinate of the end point of the transition curve, β 0 is the tangent angle of the transition curve end point, such as Figure 2 , Figure 3 shown.

[0107] For the line longitudinal section (l 0Usually the value is taken as an integer of 10m), and the high-speed railway dynamic detection filter or vehicle driving dynamics model is used to simulate the high and low long wave unevenness waveform. The minimum amplitude of high and low long wave unevenness and / or the optimal smoothness and / or the optimal vehicle driving dynamics index under actual engineering conditions are selected to determine the optimal line longitudinal section design line type, and to realize the addition of transition curves to the longitudinal section of the newly built high-speed railway line. The actual engineering conditions include: measurement technical conditions, which refer to the accuracy indicators that can be achieved by measuring the actual elevation of the longitudinal section of the line using measurement equipment; when the track structure of the line is a ballasted track, the actual engineering conditions also include the longitudinal height operation accuracy of the tamping vehicle and the maximum track lifting limit; when the track structure of the line is a ballastless track, the actual engineering conditions also include the sleeper fastener pad differential and its remaining adjustable amount.

[0108] For high-speed railway operating lines:

[0109] By changing the engineering records, the track is adjusted vertically by fine-tuning or fine-tamping operations, so as to add transition curves at both ends of the vertical curve of the longitudinal section. The main steps of the implementation of the plan are as follows:

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

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

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

[0113] S2. Fitting longitudinal section parameters

[0114] Usually, the current status of the longitudinal section of the operating line does not completely match the record parameters, and it is necessary to refit the longitudinal section parameters, including the elevation H of the slope change point. BP , slope i‰, slope length, circular curve radius R 0 .

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

[0116] Combined with the longitudinal section parameters obtained by S2 and the transition curve line type to be selected and its length and circular curve radius, the high-speed railway dynamic detection filter (filter cut-off wavelength ≥ 120m) and / or dynamic test are used to verify and calculate the transition curve line type with the minimum amplitude of track high and low long wave irregularity and / or the optimal smoothness, which is used as the initial transition curve line type. The main design indicators of the high-speed railway dynamic detection filter and the driving dynamics test are the same as those of the new high-speed railway line, and the transition curve line type to be selected is the same as the transition curve line type to be selected for the new high-speed railway line.

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

[0118] After adding the transition curve, first 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 slope sections, the design elevation of the circular curve, and the design elevation of the first and second transition curves.

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

[0120] like Figure 3 As shown, assuming that the plane mileage and elevation of the slope change point are (K BP , H BP ). Then the design elevation of any mileage K on the slope section is calculated as follows:

[0121] (9)

[0122] S4.2 Design elevation of circular curve

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

[0124] (10)

[0125] Where T is the length of the vertical curve tangent after adding the transition curve line, p is the inner displacement, R 0 is the radius of the circular curve, H desi In formula (K), the “±” is “+” for concave vertical curves and “−” for convex vertical curves.

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

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

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

[0129] (11)

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

[0131] (12)

[0132] In the formula, K BP and HBP are the horizontal mileage and elevation of the slope change point respectively; T is the length of the vertical curve tangent of the longitudinal section after adding the transition curve line type.

[0133] by Figure 4 Take as an example, calculate the mileage and elevation of any point on the first transition curve. Take the starting point ZH as the coordinate origin, the tangent through the starting point as the x-axis, the growth direction of the transition curve as the positive direction, the y-axis is determined by passing through the starting point perpendicular to the x-axis, and the bending direction of the transition curve is the positive direction of the y-axis, that is, the local coordinate system x-ZH-y of 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 and intersect it at point B. Draw a plumb line through point B, and intersect the horizontal lines through points P and ZH at points A and C respectively. Then:

[0134] In triangle C-ZH-B and triangle PAB we have

[0135] (13)

[0136] From the above formula, we can determine the lengths of ZH-C, BC, AB and AP. Then the plane mileage K of point P on the first transition curve is P and elevation H P Determined by the following formula

[0137] (14)

[0138] Taking into account the curvature direction of the first transition curve, we can get any mileage K and design elevation H of the first transition curve. desi (K) is calculated as follows:

[0139] (15)

[0140] Where x and y are the coordinates of the local coordinate system of the mathematical model of the transition curve, K and H desi The second term of the fraction (K) is “±”, the concave vertical curve is “+”, and the convex vertical curve is “−”.

[0141] Take the starting point HZ as the origin of coordinates, the tangent through the starting point as the x-axis, the growth direction of the transition curve as the positive direction, the y-axis is determined by passing through the starting point perpendicular to the x-axis, and the bending direction of the transition curve is the positive direction of the y-axis, that is, the local coordinate system of the second transition curve x-HZ-y. Similarly, any mileage K and design elevation H of the second transition curve can be obtained by sorting. desi (K) is calculated as follows:

[0142] (16)

[0143] Where x and y are the coordinates of the local coordinate system of the mathematical model of the transition curve, K and H desiThe second term of the fraction (K) is “±”, the concave vertical curve is “+”, and the convex vertical curve is “−”.

[0144] S4.4: Track vertical adjustment model

[0145] After adding transition curves at the beginning and end of the vertical curve of the longitudinal section, 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 vertical adjustment amount model of the track. The model is the horizontal mileage K, the elevation of the slope change point H BP , Circular curve radius R 0 And the length of the transition curve l 0 The nonlinear function of .

[0146] (17)

[0147] In the formula, K represents the plane mileage, H desi (K) represents the design elevation after adding the transition curve, H meas (K) indicates the actual elevation. BP represents the elevation of the slope change point, R' represents the radius of the circular curve before adding the transition curve, l 0 is the length of the added transition curve. Among them, △R is the radius change: △R=0 means that the radius of the circular curve remains unchanged after the addition of the transition curve; △R>0 means that the radius of the circular curve increases after the addition of the transition curve; △R<0 means that the radius of the circular curve decreases after the addition of the transition curve.

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

[0149] Due to the limitation of the actual adjustable amount of the track, v(K) obtained in S4 cannot usually be directly applied to track fine-tuning or fine-tamping operations. For ballastless track, the actual vertical adjustable amount of each sleeper fastener is limited, while for ballasted track, it can only be raised but not lowered. Therefore, it is necessary to verify on-site to determine the actual adjustable amounts of the track χ(K) and ζ(K).

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

[0151] S6. Optimize longitudinal section parameters

[0152] Check the track vertical adjustment calculated in S4 to determine whether it meets the requirements of the actual adjustable amount in S5. In addition, it is also necessary to check whether the minimum slope section length and the distance between the slope change point and the start and end point of the plane transition curve meet the requirements of the design specifications after the transition curve is added. If it does not meet the requirements, the selected transition curve is filtered and / or dynamically tested through the preset high-speed railway dynamic detection filter and / or driving dynamics index, and the slope change point elevation H is BP and / or circular curve radius R 0 and / or the length of the transition curve l 0 Make optimization adjustments and then repeat step S4 until all relevant requirements are met.

[0153] S6. Optimize longitudinal section parameters

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

[0155] (18)

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

[0157] (19)

[0158] In the formula, R 0 is the radius of the circular curve, Δi max is the maximum value of the algebraic difference between adjacent slope sections (‰), and V is the design speed. The distance S between the slope change point and the start and end point of the plane transition curve should be greater than the length T of the tangent line of the vertical curve after adding the transition curve line type, that is,

[0159] (20)

[0160] In the formula, K BP is the horizontal mileage of the slope change point, K Star / End is the starting or ending mileage of the plane transition curve, and T is the length of the tangent of the vertical curve after adding the transition curve line type.

[0161] In summary, for high-speed railway lines in operation, transition curves are added at both ends of the vertical curves in the longitudinal section. The track vertical adjustment model and constraint conditions can be described as follows:

[0162] (twenty one)

[0163] From formula (21), we can see that at the same mileage, different parameters H BP , R 0 and 0, the track adjustment amount is different. Therefore, it is necessary to optimize and adjust the longitudinal section parameters according to the constraint conditions of formula (21). This step is to ensure that the vertical adjustment amount of the track meets the constraint of the track adjustable amount, and it can be applied to the track fine adjustment or fine tamping operation, so that it is practical to add transition curves at both ends of the vertical curve of the longitudinal section of the operating high-speed railway. Specifically, according to the constraints, all transition curve line types that meet the constraints are calculated, and through the preset high-speed railway dynamic detection filter and / or driving dynamics index, the vertical curves after adding all transition curve line types are filtered and / or tested for driving dynamics one by one, and the optimization parameters corresponding to the longitudinal section vertical curve that meets the minimum amplitude of high and low long wave irregularity and / or the best smoothness or the best dynamic index under actual engineering conditions are selected as the longitudinal section parameters (transition curve mathematical model, transition curve length and circular curve radius) of the longitudinal section vertical curve after adding the optimal transition curve line type. The optimal solution.

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

[0165] According to the optimized longitudinal section parameters, the vertical adjustment of the track is calculated. For ballastless track, the adjustment plan is output for each sleeper to guide the track fine adjustment operation. For ballasted track, the adjustment plan is generated in *.Ver format according to specific intervals (usually 1m or 2m) and input into the automatic guided computer (Automatischer Leit Computer, ALC) of the tamping vehicle, and the tamping vehicle performs the track fine tamping operation.

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

[0167] The present invention discloses an optimization method for dynamic detection of long-wave irregularities in vertical curves of longitudinal sections of high-speed railway lines. The method is achieved by adding transition curves at both ends of the longitudinal section vertical curve, hereinafter referred to as the longitudinal section vertical curve with added transition curves. The longitudinal section vertical curve with added transition curves consists of five basic line types, namely, a front slope section, a first transition curve, a circular curve, a second transition curve and a rear slope section. Among them, the connection point between the front slope section and the first transition curve is a straight-to-slow (ZH) point, the connection point between the first transition curve and the circular curve is a gentle-circular (HY) point, the connection point between the circular curve and the second transition curve is a round-to-slow (YH) point, and the connection point between the second transition curve and the rear slope section is a gentle-to-straight (HZ) point. The present invention can solve the problems of sudden vertical acceleration changes at the beginning and end of the vertical curve of the longitudinal section of the high-speed railway track in dynamic detection and long-wave irregularities of high and low waves, and further improve the vertical smoothness of the track.

[0168] For newly built high-speed railway lines, during the line selection and design stage, according to the line design requirements, the front and rear slope sections are designed as transition curves, circular curves, and transition curve connections, and are applied to construction. For lines with different design speeds, the minimum circular curve radius of the line longitudinal section, the minimum slope section length, and the distance between the slope change point and the start and end point of the plane transition curve 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 slope section length: 800m (200~250 km / h), 900m (300~350 km / h). ③ The distance between the slope change point and the start and end point of the plane transition curve is greater than the length of the vertical curve tangent after the transition curve is added. Suppose the design line type of part of the horizontal and longitudinal section of a newly built 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 the longitudinal section parameters

[0170] like Figure 6 As shown in the figure, there are three slope change points in the section from K276 to K280. Taking the second slope change point as an example, the specific process of adding a transition curve is explained. BP =29.576m, the front slope is i‰=10.3‰, and the rear slope is i‰=6‰. The radius of the circular curve is designed to be R 0 =25000m.

[0171] Q2. Determine the initial transition curve line type

[0172] Combined with the longitudinal section parameters obtained by Q1, the cubic parabola and the one-wave sine line are selected as examples. Through the high-speed railway dynamic detection 120m high and low long wave filtering model, the waveform of the track high and low long wave unevenness is verified under the conditions of the easement curve length taking values ​​of 150m, 200m, 250m and 300m respectively, such as Figure 7 As shown. From the calculation results, when the length of the transition curve is less than 200m, the amplitude of the long wave of track height irregularity obtained by adding a third parabola is smaller. When the length of the transition curve is greater than 200m, the wavelength of the track height irregularity obtained by adding a sine parabola is longer. Assuming that the third parabola is selected as the initial transition curve line type of the longitudinal section, the steps of adding the transition curve line type are explained.

[0173] Q3. Optimize longitudinal section parameters 0

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

[0175] Then check the requirement that the vertical curve coincides with the plane transition curve. Figure 6 The mileage of the slope change point is K277+499, which is located on the plane circular curve. According to formula (8), the distance S between the slope change point and the start and end points of the plane transition curve are 301m and 341m respectively. Therefore, after adding the transition curve line type, the vertical curve tangent length T should be less than 301m. According to formula (8) and formula (9), it can be calculated that the additional transition curve should be less than 194m.

[0176] Depend on Figure 7 The track unevenness waveform obtained by simulation shows that the longer the transition curve is, the smoother the vertical curve of the longitudinal section will be. Therefore, the optimal longitudinal section design line shape has a transition curve length of l 0 190m is available. Figure 8 The comparison of the long wave unevenness of the tracks at the beginning and end of the vertical curve before and after the addition of the transition curve is given.

[0177] from Figure 8 It can be seen that at the vertical curve of the longitudinal section from K277 to K278, when there is no transition curve, the maximum amplitude of the long wave unevenness of the track is 3mm. When a cubic parabola transition curve with a length of 190m is added at the beginning and end of the vertical curve of the longitudinal section, the maximum amplitude of the long wave unevenness of the track is reduced to 0.6mm, a decrease of 80%. Therefore, adding transition curves at both ends of the vertical curve of the longitudinal section can effectively reduce the long wave unevenness of the high-speed railway track.

[0178] Taking the ballastless track of high-speed railway in operation as an example, the feasibility of adding transition curves at both ends of the vertical curve is verified, as well as the effect of reducing the high and low long wave unevenness of dynamic detection. The difference between ballasted track is that it can only start but not end the track, but the calculation ideas are basically the same.

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

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

[0181] Measure the actual elevation H of the longitudinal section reference rail meas (K), such as Fig.10 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 is the plane mileage (m), and the left vertical axis is the measured elevation (m).

[0182] S2. Fitting longitudinal section parameters.

[0183] The longitudinal section is fitted using the least square method, and the fitting deviation is as follows: Fig.10 The fitting longitudinal section results are shown in Table 1 below:

[0184] Table 1

[0185]

[0186] Judging from the fitting results, the longitudinal section parameters do not change much from the design parameters in the ledger.

[0187] S3. Select the optimal transition curve.

[0188] Using the preset high-speed railway dynamic detection filter, the filter processing and verification of the additional cubic parabola and one-wave sine line transition curves are performed, and the relationship between the peak value and standard deviation of the high and low unevenness and the increase of the transition length is statistically analyzed, such as Fig.11 As shown. Filter verification shows that under the same conditions, the longer the transition curve, the smaller the peak and standard deviation of the height irregularity, and the cubic parabola is better than a single-wave sine line. When the radius of the circular curve is 25000m and the transition curve length exceeds 100m, the peak of the height irregularity is less than 1mm and the standard deviation is less than 0.4. Therefore, the cubic parabola is selected as the optimal transition curve mathematical model, and the transition length is set to be greater than 100m.

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

[0190] For concave vertical curves, the longitudinal section parameters are fitted according to S2, H BP =24.157m, the radius is rounded to R 0 =25000m, and set l 0 =120m, and substitute into equations (9), (10), (15) and (16) to calculate the design elevations H of the front and rear slopes, circular curves and transition curves respectively. desi (K), and then the vertical adjustment of the track can be calculated according to formula (17).

[0191] For convex vertical curves, the longitudinal section parameters are fitted according to S2, H BP =88.23m, the radius is rounded to R 0=25000m, and set l 0 =120m, and substitute them into formula (17) to calculate the vertical adjustment of the track, as follows: Fig.12 shown.

[0192] Definition: Vertical adjustment of track = design elevation after adding transition curve - actual track elevation. + value indicates starting point, - value indicates end point (ballastless).

[0193] S5. Actual adjustable amount of the track.

[0194] Taking the common WJ-7 or WJ-8 fasteners as an example, the vertical adjustment range of the track is -4~+26mm. Since the actual vertical adjustable amount of each sleeper fastener is not counted, the theoretical adjustable amount of the fastener -4~+26mm is used instead of the actual adjustable amount in the calculation example, that is, χ(K)=-4mm, ζ(K)=26mm.

[0195] When the radius remains unchanged and a transition curve with a slow length of 120m is added, for the concave vertical curve, the maximum track rise is 26.5mm>ζ(K); for the convex vertical curve, the maximum track fall is -18.7mm<χ(K). Therefore, the requirements for the adjustable amount of the sleeper fasteners are not met, and the longitudinal section parameters need to be further optimized.

[0196] S6. Optimize longitudinal section parameters.

[0197] From S4, we know that if we keep the radius of the circular curve unchanged (the same as the design record) and add a transition curve with a transition length of 120, the vertical adjustment of the track of the concave vertical curve and the convex vertical curve exceeds the actual adjustable amount of the fastener, and fine adjustment cannot be performed on site. Next, reduce the radius of the circular curve or increase the length of the transition curve to optimize the longitudinal section parameters. Repeat S4 to calculate the optimized vertical adjustment of the track, such as Fig.12 As shown, the high-speed railway dynamic detection filter is used for verification. Fig.13 shown.

[0198] After optimizing the radius and the length of the transition curve, the maximum drop and maximum rise of the concave vertical curve and the convex vertical curve are -2.8mm and 14.2mm, respectively, and -3.8mm and 25.4mm. Therefore, the requirements for the adjustable amount of the sleeper fasteners are met. From the results of the dynamic detection of the 120m long wave verification, when the transition curve is not added, the peak value of the height unevenness is nearly 2.5mm, and the standard deviation is 1mm. After adding the transition curve and optimizing it, the peak value of the height unevenness is less than 1mm, and the standard deviation is less than 0.4mm. The effect of reducing the height unevenness is very significant.

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

[0200] Table 2

[0201]

[0202] From the results in Table 2, after adding the transition curve, the slope length of the longitudinal section meets the requirements of the specification. In addition, according to the requirements of the specification, the vertical curve should not overlap with the plane transition curve. The following is judged by the tangent length of the vertical curve, that is, the distance S between the slope change point and the starting point or end point of the plane transition curve should be greater than the tangent length T of the vertical curve after adding the transition curve line type. The tangent length of the vertical curve is calculated as follows:

[0203]

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

[0205] Table 3

[0206]

[0207] From the results in Table 3, after adding the transition curve, the distance between the slope change point and the starting point or end point of the plane transition curve is greater than the tangent length of the vertical curve after adding the transition curve, that is, the vertical curve does not overlap with the plane transition curve, which meets the requirements of the design specifications.

[0208] S7. Carry out track fine-tuning operations.

[0209] According to the optimized radius and transition length of S6, transition curves are added. Not only the vertical adjustment of the track is within the adjustable range, but the vertical curve setting also meets the requirements of the specifications, so track fine-tuning operations can be carried out. Fig.14 Comparison of the long wave unevenness of the track before and after adding the transition curve in accordance with S6.

[0210] By comparison, it can be found that after adding the transition curve, the long wave unevenness at the beginning and end of the vertical curve of the longitudinal section is well resolved, and the peak value of the long wave unevenness of the track height is also significantly reduced. Therefore, the method provided by the present invention can effectively reduce the long wave unevenness at the beginning and end of the vertical curve of the longitudinal section of the high-speed railway track.

[0211] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for optimizing dynamic long-wave irregularity of a high-speed railway vertical curve, characterized by: include: Obtaining a line profile type, profile parameters corresponding to the line profile type, and a transition curve to be selected, wherein the line profile type is a newly built line profile or an operating line profile; According to the preset high-speed railway dynamic detection filter and / or driving dynamics index, the vertical curves of the longitudinal section of the line after adding each transition curve are respectively subjected to filtering processing and / or dynamic testing, and the vertical curves of the longitudinal section of the line with the minimum amplitude of high and low long wave irregularities and / or the best smoothness under actual engineering conditions are selected as the initial vertical curves of the longitudinal section of the line according to the results of each filtering processing and / or testing, and the longitudinal section parameters of the initial vertical curves of the longitudinal section of the line are used as the parameters to be optimized; Selecting preset constraints according to the line profile type; when the line profile type is a newly built line profile, the constraints include a minimum slope section length constraint and a vertical curve that does not coincide with a plane transition curve; when the line profile type is an operating line profile, the constraints include a track vertical adjustable amount or a rise and fall amount constraint, a minimum slope section length constraint, and a vertical curve that does not coincide with a plane transition curve; According to the parameters to be optimized and the vertical curve of the initial line longitudinal section, the vertical curve of the line longitudinal section corresponding to all the longitudinal section parameters that meet the constraint conditions is solved, and the vertical curve of the line longitudinal section corresponding to all the parameters that meet the constraint conditions is filtered and / or tested for driving dynamics one by one through a preset high-speed railway dynamic detection filter and / or driving dynamics index, and the longitudinal section parameters that meet any one or more conditions of minimum amplitude of high and low long wave irregularities, optimal smoothness and optimal driving dynamics index under actual engineering conditions are selected as the optimal solution.

2. The method for optimizing dynamic long-wave irregularity of a high-speed railway vertical curve according to claim 1, characterized in that: Obtain the longitudinal section parameters corresponding to the line longitudinal section type, including: When the line profile type is a newly built line profile, the profile design parameters are obtained according to the high-speed railway design specification as the profile parameters, and the profile design parameters include the elevation of the slope change point, the slope section length and the circular curve radius; When the line longitudinal section type is an operating line longitudinal section, the actual elevation of the line longitudinal section is precisely measured, and the longitudinal section fitting parameters are obtained according to the actual elevation fitting of the line longitudinal section as longitudinal section parameters, and the longitudinal section fitting parameters include the elevation of the slope change point, the slope section length and the circular curve radius.

3. The method for optimizing dynamic long-wave irregularity of a high-speed railway vertical curve according to claim 1, characterized in that: According to the preset high-speed railway dynamic detection filter and / or driving dynamics index, the vertical curves of the longitudinal section of the line after adding each transition curve are filtered and / or dynamically tested, including: Calculating the mathematical model of the transition curve corresponding to each transition curve and its length and the radius of the circular curve according to the transition curve to be selected, the line longitudinal section type, and the line longitudinal section type, wherein the mathematical model of the transition curve includes a cubic parabola mathematical model, a quintic parabola mathematical model, a septad parabola mathematical model, a half-wave sine mathematical model, a single-wave sine mathematical model, and a septad quaternary mathematical model; Calculate the transition curve mathematical model corresponding to each transition curve and its length and circular curve radius, add the transition curve to the vertical curve of the line longitudinal section, and obtain the vertical curve of the line longitudinal section after adding the transition curve; By using preset high-speed railway dynamic detection filtering indicators and / or driving dynamic indicators, the vertical curves of the longitudinal section of the line after adding each transition curve are filtered and / or dynamically tested.

4. The method for optimizing dynamic long-wave irregularity of a high-speed railway vertical curve according to claim 3 is characterized by: The mathematical model of the relaxation curve includes: Cubic parabola mathematical model: ， Mathematical model of quintic parabola: ， Mathematical model of the seventh parabola: ， Half-wave sine mathematical model: ， Mathematical model of a sine wave: ， Seventh-order quaternary mathematical model: ， Where l0 is the length of the transition curve, R0 is the radius of the circular curve, x and y are the coordinates of the local coordinate system of the transition curve mathematical model. The local coordinate system takes the starting point of the transition curve as the origin, and the tangent through the starting point as the x-axis, the growth direction of the transition curve as the positive direction, and the y-axis is determined by passing through the starting point perpendicular to the x-axis, and the bending direction of the transition curve is the positive direction of the y-axis.

5. A method for optimizing dynamic long-wave irregularity of a high-speed railway vertical curve according to claim 4, characterized in that: Among the constraints: The minimum slope length constraint is: ， The constraint that the vertical curve does not coincide with the plane transition curve is: ， The vertical adjustable amount of the track is constrained as follows: ， Where L represents the length of the slope, K BP1 and K BP2 is the plane mileage of two adjacent slope change points, R0 is the radius of the circular curve, Δi is the algebraic difference (‰) between adjacent slope sections, Δi max is the maximum absolute value of Δi, V is the design speed, K BP is the horizontal mileage of the slope change point, K Star / End is the starting or ending mileage of the plane transition curve, T is the tangent length after adding the transition curve line type, p is the inward displacement, y0 is the y coordinate of the transition curve end point, β0 is the tangent angle of the transition curve end point, v(K) represents the vertical deviation of the track, 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 section of the operating line after adding the transition curve line type, H meas (K) represents the actual elevation of the vertical curve of the longitudinal section of the operating line. The vertical deviation of the track v(K) is the value of the mileage K and the elevation of the slope change point H. BP , 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 elevations of the front and rear 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 rear slope section.

6. A method for optimizing dynamic long-wave irregularity of a high-speed railway vertical curve according to claim 5, characterized in that: When the design elevation is the design elevation of the front and rear slope sections, the design elevation H desi (K) The calculation formula is: ， Where K BP and H BP are the plane mileage and elevation of the slope change point, K is the mileage of any point on the slope section, i is the slope of the slope section corresponding to the mileage K, K ZH Indicates the mileage of the vertical curve straight slow point, K HZ Indicates the mileage of the vertical curve straightening point; When the design elevation is the design elevation of the circular curve, the design elevation H desi (K) The calculation formula is: ， Where p is the inner displacement, R0 is the radius of the circular curve, H desi The first term of the fraction (K) is "±", the concave vertical curve is "+", the convex vertical curve is "−", K HY Indicates the mileage of the vertical curve transition point, K YH Indicates the mileage of the vertical curve circle slow point.

7. A method for optimizing dynamic long-wave irregularity of a high-speed railway vertical curve according to claim 6, characterized in that: When the design elevation is the design elevation of the transition curve, any mileage K and design elevation H desi (K) is calculated as follows: ， Where, T is the length of the tangent line of the vertical curve after adding the transition curve line type, i is the slope at the starting point of the transition curve, unit ‰, K and H desi The first term of the fraction (K) is "±", the first transition curve is "+", and the second transition curve is "−"; K and H desi The second term of the fraction (K) is "±", the concave vertical curve is "+", and the convex vertical curve is "−".

8. The method for optimizing dynamic long-wave irregularity of a high-speed railway vertical curve according to claim 1, characterized in that: The high-speed railway dynamic detection filter includes: passband cutoff wavelength ≥ 120m, passband maximum attenuation -3dB, stopband minimum slope 24dB / octave, driving dynamics indicators include: derailment coefficient ≤ 0.8, wheel load reduction rate ≤ 0.6, vehicle body vertical vibration acceleration ≤ 2.5m / s 2 , Sperling comfort index ≤ 2.

5.

9. A method for optimizing dynamic long-wave irregularity of a high-speed railway vertical curve according to claim 8, characterized in that: Passband cut-off wavelengths include 120m, 150m, 200m and >200m.

10. The method for optimizing dynamic long-wave irregularity of a high-speed railway vertical curve 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 measuring the actual elevation of the longitudinal section of the line using measurement equipment; Technical construction conditions. When the track structure of the line is a ballasted track, the technical construction conditions also include but are not limited to the longitudinal height operation accuracy of the tamping vehicle and the maximum track lifting amount limit. When the track structure of the line is a ballastless track, the technical construction conditions also include but are not limited to the level difference of the sleeper fastener pad and its remaining adjustable amount.

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