A track lifting scheme evaluation method based on line smoothness probability prediction after ramming

Abstract

The present application relates to the technical field of track engineering, and provides a track lifting scheme evaluation method based on line smoothness probability prediction after tamping. The method firstly determines a line analysis interval for smoothness prediction, and establishes a line state database containing track lifting quantity and track bed foundation conditions; a track bed settlement prediction model containing tamping-induced settlement and long-term cumulative deformation is constructed; the probability distribution type of model calculation parameters is determined, and grouped random assignment and spatial weighted smoothing processing are performed on multiple calculation parameters in a single iteration to generate a distribution matrix; the track bed deformation under each load action frequency is calculated based on the model; the vertical displacement of the sleeper is solved in combination with the deformation steel rail continuous beam model to obtain interval smoothness evaluation indexes containing standard deviation, chord measurement value and empty hanger number; and the confidence interval of the evaluation indexes is output through multiple iteration calculations. The present application realizes probabilistic and quantitative scientific evaluation of long-term effectiveness of the track lifting scheme.

Description

Technical Field

[0001] This invention relates to the field of track engineering technology, specifically to an evaluation method for track start-up schemes based on probabilistic prediction of track smoothness after tamping. Background Technology

[0002] Large-scale track maintenance machinery tamping is currently the core method for ballast track maintenance. It primarily improves track geometry and restores track bed elasticity through operations such as track lifting, track shifting, and clamping vibration tamping, thereby ensuring track smoothness. In recent years, precision measurement and tamping technology based on pre-set track lifting and shifting schemes has been widely applied in engineering practice. This technology effectively controls long-wave irregularities in the track by pre-inputting the optimized track lifting scheme into the tamping device control system.

[0003] However, long-term theoretical research and engineering practice have shown that ballasted track, as a granular packing structure, exhibits significant "memory" deformation characteristics. After tamping, the track geometry typically deteriorates rapidly in the initial stage until the track bed is recompacted and stabilized under repeated train loads. Therefore, using only the initial target alignment corresponding to the track-laying scheme as the evaluation basis is clearly insufficient. Even if the railway line immediately possesses good smoothness after tamping, rapid deformation during the initial stage of line operation can still lead to poor train performance in the long term, thereby forcing a significant reduction in maintenance cycles.

[0004] Current research on predicting the evolution of tamped ballast track alignment largely focuses on absolute deformation or uniform settlement at the individual sleeper level. However, in practical engineering, uniform settlement does not necessarily lead to track smoothness degradation; the essence of smoothness lies in non-uniform deformation (i.e., spatial variability) along the longitudinal direction of the track. Existing theoretical models are mostly deterministic prediction methods, which struggle to characterize the discrete and nonlinear features of deformation in ballast track sections and cannot accurately describe the time-varying laws of track geometry and orientation in continuous sections.

[0005] In summary, how to overcome the limitations of existing assessment methods that only focus on single-point absolute settlement and deterministic prediction, and fully consider the spatial variability and long-term cumulative effect of granular track bed deformation, and provide a method that can probabilistically quantify the long-term smoothness evolution law of the track after tamping, so as to achieve scientific evaluation and comparison of track-raising schemes in the long term, is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention proposes a method for evaluating track lifting schemes based on probabilistic prediction of track smoothness after tamping. This method provides a scientific basis for the quantitative comparison and selection of track lifting schemes. The specific technical solution is as follows: A method for evaluating track start-up schemes based on probabilistic prediction of track smoothness after tamping includes the following steps: S1. Obtain the track lifting scheme to be evaluated, and determine the track analysis interval for track smoothness prediction after tamping based on the track lifting scheme. S2. Establish a track status database for the track analysis section using the sleeper positions within the track analysis section as an index. The track status database includes at least the track lifting amount, ballast gradation parameters, track bed foundation conditions, and initial track elevation corresponding to the track lifting scheme. S3. Construct a track bed settlement prediction model after tamping. The track bed settlement prediction model includes a first settlement calculation item characterizing the settlement induced by tamping operation and a second settlement calculation item characterizing the long-term cumulative deformation under no-intervention conditions. The first settlement calculation item and the second settlement calculation item contain multiple calculation parameters. For the multiple calculation parameters in the track bed settlement prediction model, determine the probability distribution type of the multiple calculation parameters. S4. Perform a single iteration, using the sleeper position as an index, and randomly assign values ​​to the multiple calculation parameters in groups according to the information in the line status database. Then, perform weighted smoothing on the multiple calculation parameters after assignment in the spatial dimension to generate a distribution matrix that characterizes the spatial variability of the multiple calculation parameters along the line. S5. Based on the track bed settlement prediction model and the distribution matrix, calculate the track bed deformation at each sleeper position within the line analysis section under different load cycles, and generate a mileage-load cycle distribution matrix of track bed deformation based on the correspondence between sleeper position and mileage. S6. Based on the mileage-load action frequency distribution matrix, the deformation rail continuous beam model is used for calculation to obtain the section smoothness evaluation index of the line analysis area in a single iteration. The section smoothness evaluation index includes the standard deviation of sleeper vertical displacement, chord measurement value and the number of sleepers without load. S7. Determine whether the current iteration count has reached the preset maximum iteration count. If not, return to the step in S4 of randomly assigning values ​​to the multiple calculation parameters in groups, regenerate the distribution matrix, and perform the next iteration calculation. If the preset maximum number of iterations is reached, the confidence interval is calculated based on the interval smoothness evaluation index obtained from multiple iterations, and the evaluation result of the starting scheme to be evaluated is output.

[0007] In a preferred implementation, the expression for the settlement prediction model of the tamped track bed is:

[0008] In the formula, S represents the track bed settlement, N represents the number of load applications, and L represents the track lifting volume. The first settlement calculation item is calculated using the logarithm of the number of load applications, base 10. The calculation parameters include the ratio of tamping disturbance settlement to track lifting volume. and the settlement velocity adjustment coefficient The calculation parameters corresponding to the second settlement calculation item include the long-term settlement calculation coefficient. .

[0009] In a preferred implementation, determining the probability distribution type of each calculation parameter in the track bed settlement prediction model specifically includes: The initial distribution type and initial distribution range of the multiple calculation parameters are determined based on engineering statistical data; wherein, the proportionality coefficient The settling velocity adjustment coefficient follows a uniform distribution. The long-term settlement calculation coefficient follows a normal distribution. It follows an exponential distribution; Based on the ballast gradation parameters and track bed foundation conditions in the line status database, the mean distribution of the initial distribution range or the initial distribution type is dynamically adjusted to obtain a probability distribution of calculation parameters that matches the specific line status.

[0010] In a preferred implementation, the initial distribution type and the initial distribution range are specifically as follows: The proportionality coefficient The uniform distribution range is 0.02~0.15; The settling velocity adjustment coefficient The normal distribution has a mean of 1 and a standard deviation of 0.1. The long-term settlement calculation coefficient The exponential distribution has a mean on the order of 10. -6 ~10 -5 mm / time.

[0011] In a preferred implementation, the weighted smoothing process applied to the assigned plurality of computational parameters in the spatial dimension specifically includes: After generating random calculation parameters in each iteration, the calculation parameters of the target sleeper and the three adjacent sleepers on its left and right sides are extracted and processed using a seven-point weighted smoothing algorithm. The weighting ratios of the target sleeper and the adjacent sleepers on both sides are 0.05, 0.1, 0.2, 0.3, 0.2, 0.1 and 0.05 respectively.

[0012] In a preferred implementation, obtaining the interval smoothness evaluation index of the line analysis area in a single iteration specifically includes: Based on the mileage-load application number distribution matrix of the track bed deformation, the track bed deformation under different load application numbers is superimposed on the initial elevation of the line to obtain the track bed top surface elevation curves corresponding to different load application numbers. The elevation curve of the top surface of the track bed is used as a displacement boundary condition and input into the deformable rail continuous beam model to solve the equilibrium equations, thereby obtaining the vertical displacement of the sleeper under the corresponding number of load applications. The standard deviation and chordal value of the sleeper are calculated based on its vertical displacement, and the number of sleepers suspended without load under different load cycles is identified and counted. The standard deviation, the chord measurement value, and the number of empty sleepers are used together as the interval smoothness evaluation index for a single iteration.

[0013] In a preferred implementation, the deformable rail continuous beam model is a continuous elastic point-supported beam model, using a single-layer spring to equivalently simulate the supporting effect between the sleeper and the track bed, and taking the deformation of the track bed top surface as the displacement boundary condition. The equilibrium equation of the deformable rail continuous beam model is:

[0014] In the formula, n is the total number of nodes; and The first External forces and bending moments at each node; and The first Rail displacement and rail rotation at each node; For the first Deformation of the top surface of the track bed at each node; The elastic coefficient of the track bed; Represents the stiffness matrix of the beam element The element in the m-th row and n-th column, The expression for the stiffness matrix K of the beam element is:

[0015] In the formula, The elastic modulus of the rail; The moment of inertia of the rail section; This refers to the sleeper spacing; Here is the contact determination function, and its expression is: .

[0016] In a preferred implementation, the deformable rail continuous beam model includes a contact determination mechanism, and the specific solution process is as follows: The equilibrium equations are solved using a cyclic iterative method to obtain the rail deflection curve, and the rail displacement at each node is then determined. Is it smaller than the deformation of the top surface of the track bed? If the rail displacement at a node is less than the deformation of the ballast bed top surface, then the node is considered to have a risk of sleeper slinging without support. The difference between the ballast bed top surface deformation and the rail displacement is then calculated. The track bed elastic coefficient of the single-layer spring at its maximum point Set the stiffness to zero and iterate again based on the updated stiffness until the maximum value of the difference between the rail deformation calculated in the previous two calculations is less than the preset difference threshold; when the stable calculation result shows the difference between the deformation of the track bed top surface and the rail displacement. When the gap exceeds the preset gap threshold, it is considered that the sleeper is being hoisted empty.

[0017] Compared with the prior art, the beneficial effects of the present invention are: (1) In view of the inherent non-uniform and nonlinear deformation characteristics of crushed stone track bed as a granular accumulation structure, this invention constructs a settlement prediction model that includes tamping-induced terms and long-term cumulative terms, and performs grouped random assignment and spatial weighted smoothing on the parameters. This technical feature effectively characterizes the discreteness and spatial correlation of track bed interval deformation, and overcomes the fundamental defects of traditional deterministic prediction methods.

[0018] (2) This invention fully considers the engineering reality that "uniform settlement can still maintain track smoothness". It superimposes the generated track bed deformation matrix onto the initial elevation of the track and inputs it into the continuous elastic point support beam model of the deformed rail. The discrete deformation of a single point is transformed into a comprehensive index including the standard deviation of vertical displacement, chord measurement value and the number of unsupported sleepers. This feature comprehensively evaluates the track smoothness from two aspects: track geometry and structural support status, which is more in line with the real needs of ballast track maintenance.

[0019] (3) The calculation parameters in the settlement prediction model of this invention are not fixed constants, but are dynamically adjusted according to the subgrade type and ballast gradation parameters in the track condition database, adjusting the initial range or mean of their probability distribution. This mechanism enables the evaluation method to achieve differentiated and customized smoothness prediction for real track scenarios with different subgrade conditions and different contamination rates.

[0020] (4) This invention introduces a cyclic iterative calculation mechanism, which outputs the confidence interval of the smoothness evaluation index based on multiple prediction results of spatial variability. Compared with the existing technology that judges solely based on the initial target alignment, this method can quantitatively evaluate the long-term evolution law of track smoothness after tamping, providing a scientific basis for optimizing track start-up schemes on site, reasonably extending the tamping operation cycle, and reducing maintenance costs. Attached Figure Description

[0021] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0022] Figure 1 A flowchart illustrating a track start-up scheme evaluation method based on probabilistic prediction of track smoothness after tamping, provided for an embodiment of the present invention; Figure 2 This is a schematic diagram of the design elevation and actual elevation of the track surface in the analysis section in this embodiment of the invention; Figure 3 This is a schematic diagram of four track-starting schemes to be compared and evaluated in an embodiment of the present invention; Figure 4 This is a schematic diagram showing the track lifting amount corresponding to the four track lifting schemes in the embodiments of the present invention; Figures 5a to 5d These are schematic diagrams showing the predicted track bed deformation for track-raising schemes 1 to 4 when the loading number N=1000 times in the embodiments of the present invention. Figures 6a to 6d These are schematic diagrams showing the predicted track bed deformation for track-raising schemes 1 to 4 in the embodiments of the present invention when the loading number N=1,000,000 times. Figure 7 This is a schematic diagram of a continuous elastic point support beam model for deformable rails in an embodiment of the present invention.

[0023] In the diagram: 101, rail; 102, single-layer spring. Detailed Implementation

[0024] The present invention will be further described below through specific embodiments, but this is not a limitation of the present invention. Those skilled in the art can make various modifications or improvements based on the basic idea of ​​the present invention, but as long as they do not depart from the basic idea of ​​the present invention, they are all within the protection scope of the present invention.

[0025] A track-lifting scheme refers to a complete construction plan designed for a specific track section, encompassing the distribution of sleeper lifting volume across the entire section. It serves as the core execution basis for tamping operations using large-scale track maintenance machinery. Addressing the issue that the track bed exhibits significant "memory" deformation characteristics after ballast track tamping, making it difficult to assess long-term smoothness based solely on the initial track-lifting target alignment, this embodiment provides a track-lifting scheme evaluation method based on probabilistic prediction of post-tamping track smoothness through probabilistic prediction and spatial variability modeling.

[0026] This embodiment takes the evaluation of tamping operations in a section of ballasted track as an example, combining theoretical prediction steps with specific engineering data. This section is located on a straight uphill section with a gradient of 2‰, a design speed of 200 km / h, and is entirely laid with standard ballasted track. Figure 1 As shown, the implementation of the evaluation method specifically includes the following steps: S1. Obtain the track lifting scheme to be evaluated, and determine the track analysis section to be used for track smoothness prediction after tamping based on the track lifting scheme. Specifically, based on the actual maintenance needs on site or design drawings, a preset track shifting plan is obtained, and the track mileage range that needs to be predicted for long-term evolution is delineated as the line analysis interval.

[0027] In the specific engineering scenario of this embodiment, refer to Figure 2 This section is located on a soft roadbed and has multiple continuous track irregularities, which can be divided into three weak sections: Weak section 1 is approximately 100m long, with a maximum settlement exceeding 20.0mm; Weak section 2 is approximately 30m long, with a maximum settlement of approximately 14.0mm; and Weak section 3 is approximately 10m long, with a maximum settlement of approximately 5.1mm. The total length of the analyzed section is set at 200m, containing a total of 334 sleepers.

[0028] For this section, four alternative track starting schemes are proposed for comparison (see [reference]). Figure 3 and Figure 4 (The initial volume allocation) (1) Scheme 1: Completely restore the design alignment; (2) Track raising scheme 2: Based on scheme 1, add cosine-shaped track raising allowances with wavelengths of 100m and 30m and maximum amplitude of 5mm to weak sections 1 and 2 respectively; (3) Scheme 3: The weak section 1 is raised and fitted into a smooth curve, and the weak sections 2 and 3 are restored to the design shape; (4) Track raising scheme 4: Based on scheme 3, add the same cosine-shaped track raising reserve in weak section 1 and weak section 2 as in scheme 2.

[0029] S2. Establish a track status database for the track analysis section using the sleeper positions within the track analysis section as an index; To achieve high-precision spatial variability analysis, this embodiment follows the principle of "one track bed, one file," and the track status database includes at least: the track lifting volume corresponding to the track lifting scheme, ballast gradation parameters, track bed foundation conditions, and the initial elevation of the track.

[0030] For the 334 sleepers in this embodiment, the database contains the following information: track lifting amount (i.e., the lifting height of each sleeper during tamping operations, such as...). Figure 4 As shown); ballast gradation parameters (after investigation, it was found that the ballast in the weak section 2 was severely broken and significantly dirty due to multiple line fault alarms and reinforcement and tamping in the early stage); track bed foundation conditions (according to the analysis of monitoring data, the subgrade settlement in the analysis section has tended to converge, and the subgrade foundation can be considered to be in a stable state in subsequent analysis); and the initial elevation of the line at the corresponding mileage of each sleeper.

[0031] S3. Construct a track bed settlement prediction model after tamping; the track bed settlement prediction model includes a first settlement calculation term characterizing the settlement induced by tamping operation and a second settlement calculation term characterizing the long-term cumulative deformation under no-intervention conditions. The first and second settlement calculation terms contain multiple calculation parameters; and for the multiple calculation parameters in the track bed settlement prediction model, determine the probability distribution type of multiple calculation parameters.

[0032] Specifically, in this embodiment, the expression for the settlement prediction model of the tamped track bed is as follows:

[0033] In the formula, S represents the track bed settlement, N represents the number of load applications, and L represents the track lifting volume. The logarithm of the number of load applications to base 10; the calculation parameters corresponding to the first settlement calculation item include the ratio coefficient between tamping disturbance settlement and track lifting volume. and the settlement velocity adjustment coefficient The calculation parameters corresponding to the second settlement calculation item include the long-term settlement calculation coefficient. .

[0034] The initial distribution type and initial distribution range of multiple calculation parameters are determined based on engineering statistical data; among them, the proportionality coefficient... It follows a uniform distribution, with an initial uniform distribution range of 0.02~0.15; the settlement velocity adjustment coefficient It follows a normal distribution with a mean of 1 and a standard deviation of 0.1; long-term settlement calculation coefficient. Consider a distribution with right-skewed statistical properties, following an exponential distribution, whose mean is on the order of 10. -6 ~10 -5 mm / time.

[0035] S4. Perform a single iteration, using the sleeper position as the index, and randomly assign values ​​to multiple calculation parameters in groups according to the line status information in the line status database. Then, perform weighted smoothing on the multiple calculation parameters in the spatial dimension after assignment to generate a distribution matrix that characterizes the spatial variability of multiple calculation parameters along the line. Specifically, based on the ballast gradation parameters and track bed foundation conditions in the track status database, the mean distribution of the initial distribution range or initial distribution type is dynamically adjusted to obtain a probability distribution of calculation parameters that matches the specific track status: for sleepers with severely broken ballast in weak section 2, the adjusted probability distribution is as follows. The value range is limited to [0.05, 0.10]. Values mm / time, The sleepers follow a normal distribution with a mean of 1 and a standard deviation of 0.1. For the remaining sleepers, the value of γ ranges from [0.03, 0.08], and the value of β is 1 × 10⁻⁶. -6 mm / time, α is considered to be a normal distribution with a mean of 1 and a standard deviation of 0.1. For the remaining sleepers, γ ranges from [0.03, 0.08], and β is 1×10 -6 mm / time, α is considered to be a normal distribution with a mean of 1 and a standard deviation of 0.1.

[0036] In this embodiment, the above-mentioned assignment and smoothing process is implemented using MATLAB programming. In a single iteration calculation, multiple calculation parameters are randomly assigned values ​​in groups based on information from the track status database. Subsequently, the calculation parameters of the target sleeper and the three adjacent sleepers on each of its left and right sides are extracted and processed using a seven-point weighted smoothing algorithm. The weighting ratios of the target sleeper and its two adjacent sleepers are 0.05, 0.1, 0.2, 0.3, 0.2, 0.1, and 0.05, respectively. Through this spatial smoothing process, a distribution matrix characterizing the spatial variability of the parameters along the track is generated, truly reflecting the spatial correlation of track bed settlement.

[0037] S5. Based on the track bed settlement prediction model and distribution matrix, calculate the track bed deformation at each sleeper location within the line analysis section under different load cycles, and generate a track bed deformation mileage-load cycle distribution matrix according to the correspondence between sleeper location and mileage. This step enables the transformation from discrete parameters to continuous interval deformation. Figures 5a to 5d The distribution of track bed deformation by mileage is shown for track lifting scheme 1 to track lifting scheme 4 when the number of train loading times N=1000 times. Figures 6a to 6d The distribution of track bed deformation mileage corresponding to track lifting scheme 1 to track lifting scheme 4 is shown respectively under the condition of N=1,000,000 train loading times.

[0038] S6. Based on the mileage-load action frequency distribution matrix, the deformation rail continuous beam model is used for calculation to obtain the section smoothness evaluation index of the line analysis section in a single iteration. The section smoothness evaluation index includes the standard deviation of sleeper vertical displacement, chord measurement value and the number of sleepers without load. This step involves a comprehensive evaluation from two perspectives: the geometric shape and position of the line and the structural support condition. Specifically, it includes: S61. Superimpose the ballast deformation under different load cycles onto the initial elevation of the line to obtain the ballast top surface elevation curve under different load cycles. S62. Input the elevation curve of the track bed top surface as the displacement boundary condition into the deformable rail continuous beam model to solve the equilibrium equations. (See also...) Figure 7The deformable rail continuous beam model is a continuous elastic point-supported beam model. Rail 101 is considered a continuous beam, and a single-layer spring 102 is used to simulate the supporting effect between the sleeper and the track bed. The deformation of the track bed top surface is used as the displacement boundary condition. This model assumes that the external load is evenly distributed between the two rails 101. The equilibrium equations of the deformable rail continuous beam model are:

[0039] In the formula, n is the total number of nodes; and The first External forces and bending moments at each node; and The first Rail displacement and rail rotation at each node; For the first Deformation of the top surface of the track bed at each node; The elastic coefficient of the track bed; Represents the stiffness matrix of the beam element The element in the m-th row and n-th column, The expression for the stiffness matrix K of the beam element is:

[0040] In the formula, The elastic modulus of the rail; The moment of inertia of the rail section; This refers to the sleeper spacing; Let be the contact determination function. The expression of the contact determination function is:

[0041] S63. The equilibrium equation is solved using a cyclic iterative method to obtain the rail deflection curve, and then the vertical displacement of the sleeper under the corresponding number of load applications is obtained. The standard deviation and chord measurement values ​​(using the midpoint chord measurement method) are calculated based on the vertical displacement of the sleeper, and the number of sleepers without loads under different load applications is identified and statistically analyzed. The calculation and statistical length of the standard deviation is controlled between 25m and 200m; the chord measurement values ​​are obtained using the midpoint chord measurement method, and the chord length can be selected as 10m, 20m, 30m, 60m, or a combination thereof.

[0042] Meanwhile, the solution process, which includes the contact detection mechanism, is as follows: Determine the rail displacement at each node Is it smaller than the deformation of the top surface of the track bed? If the rail displacement at a node is less than the deformation of the ballast bed top surface, then the node is considered to have a risk of sleeper slinging without support. The difference between the ballast bed top surface deformation and the rail displacement is then calculated. The track bed elastic coefficient of the single-layer spring at the maximum point Set i to zero (i takes values ​​[1, n]), and iterate again based on the updated stiffness until the maximum value of the difference between the rail deformation calculated in the previous and next calculations is less than the preset difference threshold; when the stable calculation results show the difference between the deformation of the track bed top surface and the rail displacement When the gap exceeds the preset gap threshold, it is considered that the sleeper is being hoisted empty.

[0043] The standard deviation, chord measurement value, and number of empty sleepers are used together as evaluation indicators for the smoothness of the section in a single iteration.

[0044] In the smoothness evaluation index calculation in step S6, the specific values ​​of the relevant physical parameters are: track bed elasticity coefficient. Take 70 kN·mm -1 Rail elastic modulus Take 2.059×10 11 Pa; Moment of inertia of rail section Take 3.217×10 -5 m 4 sleeper spacing The value is set to 0.6m. The preset difference threshold (convergence condition) for the iterative solution of the continuous beam model is set to 10. -4 mm, the preset gap threshold (sleeper empty suspension judgment condition) is set to 1mm. The statistical length for standard deviation calculation is taken as 200m, and the chord length for midpoint chord measurement method is selected as 10m and 60m respectively.

[0045] S7. Determine whether the current iteration count has reached the preset maximum iteration count. If not, return to the step in S4 where multiple calculation parameters are randomly assigned to groups, regenerate the distribution matrix, and perform the next iteration calculation. If the preset maximum number of iterations is reached, the confidence interval is calculated based on the interval smoothness evaluation index obtained from multiple iterations, and the evaluation results of the starting scheme to be evaluated are output, providing a scientific basis for the optimal selection of the starting scheme.

[0046] In this embodiment, the maximum number of iterations is set to max_iter = 200. After completing all probability iterations, the smoothness prediction results at the upper limit of the 90% confidence interval are extracted. When the number of loadings N = 1000, the evaluation results are shown in Table 1; when the number of loadings N = 1,000,000, the evaluation results are shown in Table 2.

[0047] Table 1. Prediction results of line smoothness when loading times N=1000 times (upper limit of 90% confidence interval)

[0048] Table 2. Prediction results of line smoothness when loading times N=1,000,000 (upper limit of 90% confidence interval)

[0049] Based on the standard deviations and 60m chord measurements in Tables 1 and 2, track-lifting scheme 2 exhibits the best long-term track smoothness. This clearly demonstrates that appropriately setting track-lifting allowances for specific soft sections has a significant and long-lasting effect on controlling long-wave irregularities in the track. Conversely, while track-lifting scheme 1 performs reasonably well in the initial loading phase (N=1000 cycles), its smoothness degradation is more pronounced than scheme 4 after long-term operational loading (N=1,000,000 cycles). Furthermore, scheme 4 has a relatively lower total track-lifting volume, less ballast replenishment, and lower construction difficulty and cost. Considering both the long-term smoothness maintenance effect and construction economy, the system quantitatively determines that scheme 2 has the best overall benefit, followed by scheme 4. This evaluation result provides a highly reliable quantitative basis for the scientific selection of track-lifting schemes and the extension of tamping operation cycles on-site.

[0050] Finally, it should be noted that the above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for evaluating track starting schemes based on probabilistic prediction of track smoothness after tamping, characterized in that, Includes the following steps: S1. Obtain the track lifting scheme to be evaluated, and determine the track analysis interval for track smoothness prediction after tamping based on the track lifting scheme. S2. Establish a track status database for the track analysis section using the sleeper positions within the track analysis section as an index. The track status database includes at least the track lifting amount, ballast gradation parameters, track bed foundation conditions, and initial track elevation corresponding to the track lifting scheme. S3. Construct a track bed settlement prediction model after tamping. The track bed settlement prediction model includes a first settlement calculation term characterizing the settlement induced by tamping operation and a second settlement calculation term characterizing the long-term cumulative deformation under no-intervention conditions. The first settlement calculation term and the second settlement calculation term contain multiple calculation parameters. For the multiple calculation parameters in the track bed settlement prediction model, determine the probability distribution type of the multiple calculation parameters. S4. Perform a single iteration, using the sleeper position as an index, and randomly assign values ​​to the multiple calculation parameters in groups according to the line status information in the line status database. Then, perform weighted smoothing on the multiple calculation parameters after assignment in the spatial dimension to generate a distribution matrix that characterizes the spatial variability of the multiple calculation parameters along the line. S5. Based on the track bed settlement prediction model and the distribution matrix, calculate the track bed deformation at each sleeper position within the line analysis section under different load cycles, and generate a mileage-load cycle distribution matrix of track bed deformation based on the correspondence between sleeper position and mileage. S6. Based on the mileage-load action frequency distribution matrix, the deformation rail continuous beam model is used for calculation to obtain the section smoothness evaluation index of the line analysis area in a single iteration. The section smoothness evaluation index includes the standard deviation of sleeper vertical displacement, chord measurement value and the number of sleepers without load. S7. Determine whether the current iteration count has reached the preset maximum iteration count. If not, return to the step in S4 of randomly assigning values ​​to the multiple calculation parameters in groups, regenerate the distribution matrix, and perform the next iteration calculation. If the preset maximum number of iterations is reached, the confidence interval is calculated based on the interval smoothness evaluation index obtained from multiple iterations, and the evaluation result of the starting scheme to be evaluated is output.

2. The method for evaluating track starting schemes based on probabilistic prediction of track smoothness after tamping, as described in claim 1, is characterized in that, The expression for the settlement prediction model of the tamped track bed is as follows: In the formula, S represents the track bed settlement, N represents the number of load applications, and L represents the track lifting volume. The first settlement calculation item is calculated using the logarithm of the number of load applications, base 10. The calculation parameters include the ratio of tamping disturbance settlement to track lifting volume. and the settlement velocity adjustment coefficient The calculation parameters corresponding to the second settlement calculation item include the long-term settlement calculation coefficient. .

3. The method for evaluating track starting schemes based on probabilistic prediction of track smoothness after tamping, as described in claim 2, is characterized in that... Determining the probability distribution type of each calculation parameter in the track bed settlement prediction model specifically includes: The initial distribution type and initial distribution range of the multiple calculation parameters are determined based on engineering statistical data; wherein, the proportionality coefficient The settling velocity adjustment coefficient follows a uniform distribution. The long-term settlement calculation coefficient follows a normal distribution. It follows an exponential distribution; Based on the ballast gradation parameters and track bed foundation conditions in the line status database, the mean distribution of the initial distribution range or the initial distribution type is dynamically adjusted to obtain a probability distribution of calculation parameters that matches the specific line status.

4. The method for evaluating track starting schemes based on probabilistic prediction of track smoothness after tamping, as described in claim 3, is characterized in that... The initial distribution type and initial distribution range are specifically as follows: The proportionality coefficient The uniform distribution range is 0.02~0.15; The settling velocity adjustment coefficient The normal distribution has a mean of 1 and a standard deviation of 0.

1. The long-term settlement calculation coefficient The exponential distribution has a mean on the order of 10. -6 ~10 -5 mm / time.

5. The method for evaluating track starting schemes based on probabilistic prediction of track smoothness after tamping, as described in claim 1, is characterized in that... The weighted smoothing process performed on the assigned multiple calculation parameters in the spatial dimension specifically includes: After generating random calculation parameters in each iteration, the calculation parameters of the target sleeper and the three adjacent sleepers on its left and right sides are extracted and processed using a seven-point weighted smoothing algorithm. The weighting ratios of the target sleeper and the adjacent sleepers on both sides are 0.05, 0.1, 0.2, 0.3, 0.2, 0.1 and 0.05 respectively.

6. The method for evaluating track starting schemes based on probabilistic prediction of track smoothness after tamping, as described in claim 1, is characterized in that... The method of obtaining the interval smoothness evaluation index of the line analysis area in a single iteration specifically includes: Based on the mileage-load application number distribution matrix of the track bed deformation, the track bed deformation under different load application numbers is superimposed on the initial elevation of the line to obtain the track bed top surface elevation curves corresponding to different load application numbers. The elevation curve of the top surface of the track bed is used as a displacement boundary condition and input into the deformable rail continuous beam model to solve the equilibrium equations, thereby obtaining the vertical displacement of the sleeper under the corresponding number of load applications. The standard deviation and chordal value of the sleeper are calculated based on its vertical displacement, and the number of sleepers suspended without load under different load cycles is identified and counted. The standard deviation, the chord measurement value, and the number of empty sleepers are used together as the interval smoothness evaluation index for a single iteration.

7. The method for evaluating track starting schemes based on probabilistic prediction of track smoothness after tamping, as described in claim 6, is characterized in that... The deformable rail continuous beam model is a continuous elastic point-supported beam model. A single-layer spring is used to simulate the supporting effect between the sleeper and the track bed. The deformation of the track bed top surface is used as the displacement boundary condition. The equilibrium equations of the deformable rail continuous beam model are: In the formula, n is the total number of nodes; and The first External forces and bending moments at each node; and The first Rail displacement and rail rotation at each node; For the first Deformation of the top surface of the track bed at each node; The elastic coefficient of the track bed; Represents the stiffness matrix of the beam element The element in the m-th row and n-th column, The expression for the stiffness matrix K of the beam element is: In the formula, The elastic modulus of the rail; The moment of inertia of the rail section; This refers to the sleeper spacing; Here is the contact determination function, and its expression is: 。 8. The method for evaluating track starting schemes based on probabilistic prediction of track smoothness after tamping, as described in claim 7, is characterized in that... The deformable rail continuous beam model includes a contact determination mechanism, and the specific solution process is as follows: The equilibrium equations are solved using a cyclic iterative method to obtain the rail deflection curve, and the rail displacement at each node is then determined. Is it smaller than the deformation of the top surface of the track bed? ; If the rail displacement at a node is less than the deformation of the ballast bed top surface, then the node is considered to have a risk of sleeper slack. The difference between the ballast bed top surface deformation and the rail displacement is calculated. The track bed elastic coefficient of the single-layer spring at its maximum point Set the stiffness to zero and iterate again based on the updated stiffness until the maximum value of the difference between the rail deformation calculated in the previous two calculations is less than the preset difference threshold; when the stable calculation result shows the difference between the deformation of the track bed top surface and the rail displacement. When the gap exceeds the preset gap threshold, it is considered that the sleeper is being hoisted empty.

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