A method for determining percentiles of irregularity spectrum of high-speed railway ballastless track

Abstract

The present invention discloses a method for determining percentiles of the unevenness spectrum of a high-speed railway ballastless track, which takes into account the statistical characteristics of the unevenness frequency domain of the high-speed railway ballastless track, and can determine the percentile α of the track unevenness spectrum corresponding to the track smoothness of the target section, overcoming the problem that the smoothness management value of the high-speed railway ballastless track in the specification only considers a specific chord length and is difficult to fully reflect the frequency domain characteristics of the track unevenness. According to the present invention, the percentile α of the track unevenness spectrum is determined, and it is only necessary to perform leveling measurement on the rail surface of the target section of the line, and the percentile α of the track unevenness spectrum can be simply and quickly calculated, which is convenient for engineering application, and compared with the statistical determination method based on the unevenness detection data of the track inspection vehicle, it significantly reduces the cost and effectively saves time.

Description

Technical Field

[0001] The invention belongs to the technical field of railway track engineering, and in particular relates to a method for determining percentiles of the unevenness compliance spectrum of a high-speed railway ballastless track. Background Art

[0002] The operating speed of high-speed railways is much higher than that of conventional railways. Ballastless tracks with strong integrity and less maintenance are widely used, which puts higher requirements on the smoothness of the track structure and the dynamic stability of the roadbed structure. Therefore, maintaining the high smoothness of the track structure is an important prerequisite for the safe and smooth operation of high-speed trains. The quantitative evaluation method of track surface unevenness is the technical key to track smoothness control.

[0003] The current railway industry-related specifications often control track smoothness from two aspects: static geometric deviation and dynamic unevenness. Static height deviation is usually controlled by chord measurement or distance difference method based on the value of the sag under a certain chord length, and corresponding management values ​​are formulated. For example, the "TG / GW 115-2012 High-speed Railway Ballastless Track Line Maintenance Rules (Trial)" stipulates that the static height deviation of 250-350km / h lines is controlled by the maximum chord sag of 10m and below, and the management values ​​at the levels of operation acceptance, regular maintenance, temporary repairs, and speed limit (200km / h) are 2, 4, 7, and 8mm respectively. The evaluation of dynamic unevenness is often based on the detection data of the track inspection vehicle. After filtering in a certain wavelength range, it is controlled according to the half-peak value of the actual amplitude. For example, the "TB10761-2013 Technical Specifications for Dynamic Acceptance of High-Speed ​​Railway Projects" stipulates that for 250-350km / h lines, under the conditions of track unevenness management levels I and II, the acceptance management values ​​for wavelengths of 1.5-42m are 3mm and 5mm, and the acceptance management values ​​for wavelengths of 1.5-120m are 5mm and 7mm.

[0004] Track irregularity spectrum contains the frequency spectrum information of track irregularity and is a common method to describe the statistical characteristics of track irregularity in the frequency domain. Since track irregularity spectrum has similarity, the track irregularity spectrum under different smoothness is a family of curves with consistent trends. Statistical data show that the ratio of the amplitude of track irregularity spectrum of different frequencies to its average spectrum (α = 63.2%) satisfies the χ2 equation with 2 degrees of freedom. 2 Probability distribution. The larger the amplitude of the track irregularity spectrum, the worse the line smoothness. Therefore, the track irregularity spectrum percentile can be used to quantitatively evaluate track smoothness.

[0005] The vector or amplitude at a specific chord length and the percentile of the track irregularity spectrum are both quantitative descriptions of track smoothness, but there is currently no research on the correspondence between the two methods. The standard method only considers the irregularity at a specific chord length or spatial frequency, and does not consider the statistical characteristics of track irregularity in the full frequency band. The method of determining the percentile based on the statistical data of the track irregularity spectrum relies on a large amount of track inspection data and professional track inspection equipment, and there is no corresponding relationship with the irregularity management value in the current railway industry-related specifications, which makes it difficult to apply it to engineering practice. Summary of the invention

[0006] In view of the above-mentioned deficiencies in the prior art, the method for determining the percentile of the height and low unevenness spectrum of the high-speed railway ballastless track provided by the present invention solves the problem that the smoothness management value of the high-speed railway ballastless track in the existing specifications only considers the specific chord length and is difficult to fully reflect the frequency domain characteristics of the track unevenness.

[0007] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is: a method for determining the percentile of the unevenness spectrum of high-speed railway ballastless track, comprising the following steps:

[0008] S1. Collect track surface elevation data of target sections with uneven height of high-speed railway ballastless track;

[0009] S2. Determine the vector index at each chord length based on the rail surface elevation data;

[0010] S3. Determine the percentile of the unevenness spectrum at each chord length based on the vector index;

[0011] S4. According to the percentile of the height and low roughness spectrum, determine the percentile of the height and low roughness spectrum that affects driving safety and stability, and obtain the percentile of the track roughness spectrum of the target section by weighted average.

[0012] Furthermore, in step S1, the track elevation data h of the target section with a total length of 200 m is obtained by leveling at intervals of 5 m. i (i=0,1,…,40), i is the ordinal number of the fastener node divided into the target road section.

[0013] Furthermore, the step S2 is specifically as follows:

[0014] S21, according to the track surface elevation data h i (i=0,1,…,40), with 5m interval, determine the chord length L k The mid-span vector sequence d k Among them, L k =10m×k, k=1,2,…,12, k is the ordinal number of the chord length.

[0015] S22, with the uneven average spectrum of high and low k Standard value of the maximum mid-span sagitta As a reference, determine the chord length L k The vector index η k ;

[0016]

[0017] In the formula, Δ k is the vector sequence d of each span k The maximum value among , k=1,2,…,12.

[0018] Furthermore, in step S22, the maximum mid-span sagittal standard value They are 1.44, 1.87, 2.30, 2.75, 3.23, 3.71, 4.17, 4.63, 5.02, 5.37, 5.64 and 5.86 mm respectively.

[0019] Furthermore, in step S3, the chord length L k The percentile α of the lower unevenness spectrum k for:

[0020]

[0021] Furthermore, the step S4 is specifically as follows:

[0022] S41, according to the wheel-rail additional force weight m k , determine the percentiles of the roughness spectrum that affect driving safety

[0023] S42, according to the vehicle body acceleration weight n k , determine the percentile of the roughness spectrum that affects driving stability

[0024] S43. According to the limit ratio of wheel-rail force to vehicle acceleration, p With α a The weighted average is used to obtain the track irregularity spectrum percentile α of the target section.

[0025] Furthermore, in step S41, the wheel-rail additional force weight m k They are 0.462, 0.199, 0.071, 0.043, 0.026, 0.016, 0.016, 0.014, 0.024, 0.035, 0.048 and 0.046 respectively.

[0026] Furthermore, in step S42, the vehicle acceleration weight n k(k=1,2,…,12) are 0.107, 0.060, 0.017, 0.045, 0.059, 0.086, 0.108, 0.122, 0.124, 0.110, 0.086 and 0.075 respectively.

[0027] Furthermore, in step S43, α p With α a The weighted coefficients for weighted average are 0.51 and 0.49 respectively.

[0028] The beneficial effects of the present invention are:

[0029] (1) The present invention takes into account the statistical characteristics of the unevenness of high-speed railway ballastless tracks in the frequency domain and determines the percentiles of the track unevenness spectrum for quantifying the track smoothness based on the chord measurement method for static geometry deviation control of tracks in the current specification. This overcomes the problem that the smoothness management value of high-speed railway ballastless tracks in the specification only considers a specific chord length and is difficult to fully reflect the frequency domain characteristics of track unevenness.

[0030] (2) The present invention can simply and quickly determine the percentiles of the high and low track irregularity spectra by only performing leveling measurements on the target section of the line, which is convenient for engineering applications. Compared with the statistical determination method based on the irregularity detection data of the track inspection vehicle, it significantly reduces the cost and effectively saves time. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 A flow chart of a method for determining percentiles of the unevenness spectrum of high-speed railway ballastless track provided by the present invention.

[0032] Figure 2 A schematic diagram of leveling measurement provided by the present invention.

[0033] Figure 3 This is the transfer function of the midpoint chord measurement method provided by the present invention.

[0034] Figure 4 The present invention provides a relationship curve between the track irregularity spectrum percentile α and the high and low irregularity vector Δ under different methods.

[0035] Figure 5 The present invention provides a curve of the relationship between the track irregularity spectrum percentile α and the vector index η.

[0036] Figure 6 The present invention provides an average spectrum amplitude curve of the height irregularity of the ballastless track.

[0037] Figure 7 The typical mid-span maximum value Δ provided by the present invention k Histograms and distribution fitting.

[0038] Figure 8The wheel-rail additional force and the vehicle body acceleration normalized weights according to the chord length L provided by the present invention are k Change curve.

[0039] Fig. 9 It is the calculation result of the track irregularity spectrum percentile α of the measured track surface elevation provided by the present invention. DETAILED DESCRIPTION

[0040] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0041] Embodiment 1:

[0042] The embodiment of the present invention provides a method for determining the percentile of the unevenness spectrum of a high-speed railway ballastless track, such as Figure 1 As shown, the following steps are included:

[0043] S1. Collect track surface elevation data of target sections with uneven height of high-speed railway ballastless track;

[0044] S2. Determine the vector index at each chord length based on the rail surface elevation data;

[0045] S3. Determine the percentile of the unevenness spectrum at each chord length based on the vector index;

[0046] S4. According to the percentile of the roughness spectrum, determine the percentile of the roughness spectrum that affects driving safety and smooth operation, and obtain the percentile of the track roughness spectrum of the target section by weighted average.

[0047] In step S1 of the embodiment of the present invention, the track surface elevation data h of the target section with a total length of 200 m is obtained by leveling at intervals of 5 m. i (i=0,1,…,40), i is the ordinal number of the fastener node divided into the target road section.

[0048] Step S2 of the embodiment of the present invention is specifically as follows:

[0049] S21, according to the track surface elevation data h i (i=0,1,…,40), with 5m interval, determine the chord length L k The mid-span vector sequence d k Among them, L k =10m×k, k=1,2,…,12, k is the ordinal number of the chord length.

[0050] S22, with the uneven average spectrum of high and low k Standard value of the maximum mid-span sagitta As a reference, determine the chord length L k The vector index η k ;

[0051]

[0052] In the formula, Δ k is the vector sequence d of each span k The maximum value among , k=1,2,…,12.

[0053] In step S22 of this embodiment, the average spectrum of high and low irregularities in the chord length L is calculated based on the irregularity spectrum of TB / T 3352-2014 High-speed Railway Ballastless Track. k (L k =10m×k, k=1,2,…,12) under the standard value of the maximum mid-span vector As the benchmark, the maximum mid-span sagittal standard value They are 1.44, 1.87, 2.30, 2.75, 3.23, 3.71, 4.17, 4.63, 5.02, 5.37, 5.64 and 5.86 mm respectively.

[0054] In step S3 of the embodiment of the present invention, the chord length L k The percentile α of the lower unevenness spectrum k for:

[0055]

[0056] Step S4 of the embodiment of the present invention is specifically as follows:

[0057] S41, according to the wheel-rail additional force weight m k , determine the percentiles of the roughness spectrum that affect driving safety

[0058] S42, according to the vehicle body acceleration weight n k , determine the percentile of the roughness spectrum that affects driving stability

[0059] S43. According to the limit ratio of wheel-rail force to vehicle acceleration, p With α a The weighted average is used to obtain the track irregularity spectrum percentile α of the target section.

[0060] In step S41 of this embodiment, the wheel-rail additional force weight m kThey are 0.462, 0.199, 0.071, 0.043, 0.026, 0.016, 0.016, 0.014, 0.024, 0.035, 0.048 and 0.046 respectively.

[0061] In step S42 of this embodiment, the vehicle acceleration weight n k (k=1,2,…,12) are 0.107, 0.060, 0.017, 0.045, 0.059, 0.086, 0.108, 0.122, 0.124, 0.110, 0.086 and 0.075 respectively.

[0062] In step S43 of this embodiment, α p With α a The weighted coefficients for weighted average are 0.51 and 0.49 respectively.

[0063] Embodiment 2:

[0064] The embodiment of the present invention provides a specific example of the method for determining the percentile of the unevenness spectrum in embodiment 1:

[0065] In step S1 of the embodiment of the present invention, the rail surface elevation data is obtained by leveling, such as Figure 2 As shown in the figure, a continuous section of 200m in a straight line with a single longitudinal slope is selected as the measurement range in the target section. The fastener section near the middle position is taken as the base point, and extended to both sides of the longitudinal direction of the line by 160 times the fastener node spacing (about 100m long), with a total length of 200m, which is consistent with the calculation unit length of the track irregularity quality index TQI for evaluating the quality of track geometric status sections in "TB 10761-2013 Technical Specifications for Dynamic Acceptance of High-speed Railway Projects". The track surface elevation data of 41 fastener node sections are measured at intervals of 5m (8 times the fastener node spacing).

[0066] In the present invention, the chord length L is used k The midpoint chord measurement method under the condition of obtaining the maximum value of the mid-span vector Δ k . Through the chord length L k The midpoint chord measurement method can obtain the mid-span vector sequence d k , take the maximum value of Δ k ; mid-span vector sequence d k The vertical height difference between the midpoint of the chord and the actual track surface at the same longitudinal position is measured. The track surface elevation at the midpoint of the chord is measured as h. i The elevations of the two end points of the chord are The corresponding mid-span vector value d ki :

[0067]

[0068] By Fourier transforming the above equation, we can get the transfer function H(ω) of the midpoint chord measurement method:

[0069]

[0070] In the formula, is the Fourier transform, j is the imaginary unit, and the chord length L k The transfer function H(ω) of the midpoint chord measurement method is as follows: Figure 3 As shown. The chord length L is when the frequency domain amplitude magnification factor is greater than 1. k The effective measurement frequency band of the midpoint chord measurement method is: k The corresponding effective measurement wavelength range is

[0071] Considering that the upper limit of the track spectrum wavelength in the current "TB / T 3352-2014 High-speed Railway Ballastless Track Irregularity Spectrum" is 200m, and the maximum detection wavelength of the dynamic track inspection vehicle is 120m, which is a low-frequency long wave that includes track irregularities, the maximum chord length of the midpoint chord measurement method is 120m. At the same time, since the interval of the leveling measurement is 5m, the chord length of the chord measurement method can only be a multiple of 10m, that is, all possible values ​​of the chord length L are 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120m, and the chord length L k Corresponding to the different spatial frequencies of track irregularities. Since track irregularities are random, the chord length L k The mid-span vector sequence d k Random distribution, usually the maximum value of the mid-span vector Δ in the section k As an evaluation indicator.

[0072] In step S3 of the embodiment of the present invention, the chord length L k The percentile α of the lower unevenness spectrum k for:

[0073]

[0074] In the present invention, based on the random simulation of track height irregularity, the relationship between the track irregularity spectrum percentile α and the normalized vector index η is determined. According to the "TB 10761-2013 Technical Specifications for Dynamic Acceptance of High-speed Railway Engineering", through the simulation of track height irregularity, it can be obtained that under the conditions of the smoothness control methods such as the 10m chord maximum vector method, the 5m / 30m chord vector distance difference method, and the 150m / 300m chord vector distance difference method, the track irregularity spectrum percent α has a nonlinear growth curve with the height irregularity vector Δ, such as Figure 4 Taking the roughness index under the condition of average spectrum α = 63.2% as reference, the generalized extreme value (GEV) distribution model is used for fitting, and the relationship between α and normalized vector index η is obtained, that is, like Figure 5 shown.

[0075] therefore

[0076] In step S3 of the embodiment of the present invention, the maximum mid-span sagittal standard value They are 1.44, 1.87, 2.30, 2.75, 3.23, 3.71, 4.17, 4.63, 5.02, 5.37, 5.64 and 5.86 mm respectively.

[0077] In the present invention, in order to obtain the maximum mid-span sagittal standard value by Figure 6 Based on the average spectrum (α=63.2%) in the specification of TB / T 3352-2014 High-speed Railway Ballastless Track Irregularity Spectrum, 2000 track surface irregularity samples were randomly generated, and the chord length L was counted. k The maximum mid-span vector Δ k , its typical statistical histogram is as follows Figure 7 As shown. For the maximum mid-span vector under the average spectrum condition Δ k The generalized extreme value (GEV) distribution model is used for fitting, and the morphological parameter ξ, location parameter μ, and scale parameter β are obtained. The quantile value corresponding to the maximum probability density is taken as the maximum mid-span vector standard value. Right now Chord length L k The maximum mid-span sagittal standard value under See Table 1.

[0078] Table 1: Standard values ​​of maximum mid-span angular displacement corresponding to the average spectrum of high-speed railway ballastless track

[0079]

[0080] In step S41 of the embodiment of the present invention, the wheel-rail additional force weight m k (k=1,2,…,12) are 0.462, 0.199, 0.071, 0.043, 0.026, 0.016, 0.016, 0.014, 0.024, 0.035, 0.048 and 0.046 respectively.

[0081] In step S42 of the embodiment of the present invention, the vehicle acceleration weight n k (k=1,2,…,12) are 0.107, 0.060, 0.017, 0.045, 0.059, 0.086, 0.108, 0.122, 0.124, 0.110, 0.086 and 0.075 respectively.

[0082] In the present invention, the typical dynamic response of a vehicle under a single cosine type irregularity condition is used to analyze the dynamic response of the vehicle under different chord lengths L. k The percentile α under k Weighted average. Dynamic simulation is performed under the excitation of cosine type irregularities with the same amplitude and wavelength l of 10 to 200m, and the dynamic responses such as wheel-rail contact force and vehicle body acceleration are obtained. Consider the chord length L k The effective wavelength corresponding to the midpoint chord measurement method is Take the interval average value as the equivalent wavelength l k , i.e. l k =1.3l k ,like Figure 8 As shown. It can be obtained that the wheel-rail additional force weight m k (k=1,2,…,12) are 0.462, 0.199, 0.071, 0.043, 0.026, 0.016, 0.016, 0.014, 0.024, 0.035, 0.048, 0.046 respectively; the vehicle acceleration weight n k (k=1,2,…,12) are 0.107, 0.060, 0.017, 0.045, 0.059, 0.086, 0.108, 0.122, 0.124, 0.110, 0.086 and 0.075 respectively.

[0083] In the embodiment of the present invention, in step S43, α p With α a The weighted coefficients are 0.51 and 0.49 respectively.

[0084] In the present invention, α p With α a They are the percentiles of the track spectrum determined by driving safety and riding comfort, respectively. In actual operation, both are key to the control of good service performance of high-speed railways. According to the "TB10761-2013 Technical Specifications for Dynamic Acceptance of High-Speed ​​Railway Projects", the reference value of wheel-rail vertical force control is 120kN, and the vertical vibration acceleration of the car body is not more than 1.0m / s 2 The dynamic simulation results under the excitation of cosine type irregularities with a wavelength L of 10 to 200 m show that the limit ratio of the maximum value of the wheel-rail vertical force is 65.75%; the limit ratio of the maximum value of the vehicle body vertical acceleration is 63.00%. p With α a , and the weight coefficients are 0.51 and 0.49 respectively.

[0085] Embodiment 3:

[0086] This embodiment provides a verification example of the determination method in the above embodiment:

[0087] In this embodiment, in the field comprehensive tests of ballastless track lines such as Qinshen Passenger Dedicated Line, Beijing-Tianjin Intercity Railway, Suiyu Line ballastless track, Wuhan-Guangzhou Passenger Dedicated Line, etc., the track surface elevation data of some test sections were recorded, and the corresponding track irregularity spectrum percentile α was calculated by the present invention. The results are shown in Table 2 and Fig. 9 shown.

[0088] Table 2 Percentile α of track irregularity spectrum corresponding to the measured track surface elevation of high-speed railway ballastless track

[0089]

[0090]

[0091] The track irregularity spectrum percentile α value calculated by the present invention has a small difference between the left and right tracks in the same target section, which can better reflect the smoothness level of the target section. Based on the above analysis, the method for determining the train load dynamic coefficient of the high-speed railway ballastless track subgrade provided by the present invention is reasonable and feasible.

[0092] The present invention obtains the track elevation data of the target section by leveling, and obtains the vector index η under different chord lengths by chord measurement and normalization technology. k , using nonlinear regression method, determine the percentile α of the unevenness spectrum under different chord lengths k Based on the data weighting method of wheel-rail additional force and vehicle vertical acceleration, the track irregularity spectrum percentile α of the target section is determined. This method has a wide range of applications, is convenient and fast, and has reliable results. It can be quickly applied to the inspection and analysis of the smoothness of ballastless track structures.

[0093] The present invention uses specific embodiments to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

[0094] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A method for determining the percentile of the unevenness spectrum of high-speed railway ballastless track, characterized in that: The following steps are involved: S1. Collect track surface elevation data of target sections with uneven height of high-speed railway ballastless track; S2. Determine the vector index at each chord length based on the rail surface elevation data; S3. Determine the percentile of the unevenness spectrum at each chord length based on the vector index; S4. Determine the percentile of the roughness spectrum that affects driving safety and stability according to the percentile of the roughness spectrum at each chord length, and obtain the percentile of the track roughness spectrum of the target section by weighted average. In step S1, the track elevation data h of the target section with a total length of 200 m is obtained by leveling at intervals of 5 m. i , i=0,1,…,40, i is the ordinal number of the fastener node divided into the target road section; The step S2 is specifically as follows: S21, according to the track surface elevation data h i , with 5m intervals, determine the chord length L k The mid-span vector sequence d k Among them, L k =10m×k, k=1,2,…,12, k is the ordinal number of the chord length; S22, with the uneven average spectrum of high and low k Standard value of the maximum mid-span sagitta As a reference, determine the chord length L k The vector index η k ; In the formula, Δ k is the vector sequence d at each span k The maximum value among them, k=1,2,…,12; In step S3, the chord length L k The percentile α of the lower unevenness spectrum k for: The step S4 is specifically as follows: S41, according to the wheel-rail additional force weight m k , determine the percentiles of the roughness spectrum that affect driving safety S42, according to the vehicle body acceleration weight n k , determine the percentile of the roughness spectrum that affects driving stability S43. According to the limit ratio of wheel-rail force to vehicle acceleration, p With α a The weighted average is used to obtain the track irregularity spectrum percentile α of the target section.

2. The method for determining the percentile of the unevenness spectrum of high-speed railway ballastless track according to claim 1 is characterized in that: In step S22, the maximum mid-span sagittal standard value They are 1.44, 1.87, 2.30, 2.75, 3.23, 3.71, 4.17, 4.63, 5.02, 5.37, 5.64 and 5.86 mm respectively.

3. The method for determining the percentile of the unevenness spectrum of high-speed railway ballastless track according to claim 1 is characterized in that: In step S41, the wheel-rail additional force weight m k They are 0.462, 0.199, 0.071, 0.043, 0.026, 0.016, 0.016, 0.014, 0.024, 0.035, 0.048 and 0.046 respectively.

4. The method for determining the percentile of the unevenness spectrum of high-speed railway ballastless track according to claim 1 is characterized in that: In step S42, the vehicle acceleration weight n k They are 0.107, 0.060, 0.017, 0.045, 0.059, 0.086, 0.108, 0.122, 0.124, 0.110, 0.086 and 0.075 respectively.

5. The method for determining the percentile of the unevenness spectrum of high-speed railway ballastless track according to claim 1 is characterized in that: In step S43, p With α a The weighted coefficients for weighted average are 0.51 and 0.49 respectively.

Images