A two-stage optimization method for rail state control

Abstract

The present invention discloses a two-stage optimization method for rail state control, which belongs to the application category of precision engineering measurement technology in the field of rail transportation. The rail to be optimized is segmented in the first stage, and a rail state optimization model containing typical sensitive wavelength irregularities is established; additional sleeper fastener adjustment amount restrictions and constraint boundaries are added, and the inequality constraint model is solved section by section; the inequality is iteratively corrected according to the evaluation value until the iteration is terminated; the optimal real number solution is obtained based on the smoothing information; the second stage is segmented, and a state optimization model containing the n-order difference function of the residual deviation of the neighborhood point and the waveform consistency function is established; additional sleeper fastener adjustment amount restrictions and constraint boundaries are added, and the inequality constraint model is solved section by section to obtain the optimal differential integer solution. The present invention takes into account the variable wavelength irregularities that cause train excitation and the problem of adjusting material grade differences in general engineering, improves ride comfort, reduces TQI, solves the problem that the formulation of fine-tuning plans is time-consuming and labor-intensive, and the effects are uneven, and realizes optimal state control.

Description

Technical Field

[0001] The present invention relates to the technical field of railway track precision engineering measurement, and in particular to a two-stage optimization method for rail state control. Background Art

[0002] Ensuring high smoothness by developing optimized rail shape and position adjustment plans is key to high-speed, safe, and smooth train operation. From fine-tuning of bi-block ballastless track tracks or slab ballastless track plates during the construction phase to fine-tuning of long rails and track during the operational and maintenance phases, static adjustment acceptance criteria include lateral / vertical deviation, height / track irregularity at fixed wavelengths such as 10m, 20m, 30m, and 300m chords, and several types of horizontal / gauge and twist / gauge change rates. With the transition from the construction phase to the operational and maintenance phase, track smoothness requirements become more stringent and complex. Existing track fine-tuning plans rely on random software, which has shortcomings in theoretical models, processing methods, and adjustment results. These include low automation, time-consuming and labor-intensive processes, and suboptimal control of track smoothness. "A Method for Optimizing Rail Smoothness" (Application No. 202210394546.4) proposes to optimize the adjustment amount of rail fasteners in segmented planning units, gradually achieve smoothness control of the overall rail state, and obtain an optimized solution. The stepless adjustment at this stage can greatly improve the track state and improve its smoothness under the requirements of the fixed-wavelength unevenness index specified in the existing specifications, but the implementation effect will be limited by the existing construction conditions. In the maintenance and optimization of track smoothness, in order to save costs and facilitate the modularization of pad fasteners, multiple pads with a step difference of 0.5mm or 1.0mm are often used to change the shape and position of the track to achieve the purpose of improving the state. If construction personnel rely on experience and use a simple rounding method to approximate the stepless adjustment fine-tuning scheme, the smoothness effect of the adjusted rail state will be reduced, and even the dilemma of excessive unevenness will occur. Therefore, two further issues need to be addressed: ① To reduce the TQI, minimize train shaking and vibration, and further improve passenger comfort, the impact of variable-wavelength unevenness that causes train excitation needs to be considered and incorporated into the optimization model for effective control; ② Taking into account the problem that the thickness of the pads in the fastener system used for rail geometry adjustment has graded differences of 0.5 mm and 1.0 mm, the stepless adjustment scheme should be effectively converted to a graded adjustment scheme to ensure that the track state loss before and after the conversion is as small as possible and the track state is as smooth as possible after the graded adjustment is implemented. Summary of the Invention

[0003] To address the above issues, the present invention aims to provide a two-stage optimization method for rail state control. This method ensures high rail smoothness through a first-stage stepless optimization adjustment. Furthermore, a second-stage differential optimization adjustment is implemented. By using nth-order difference constraints on the residual deviations of neighboring points and waveform consistency constraints, the rail state of the stepless adjustment is ensured to be inherited as completely as possible from the rail state of the differential adjustment. In the first stage, the stepless adjustment uses the objective function, the typical sensitive wavelength irregularity function, and the rail state evaluation function as the optimization model. The entire rail to be adjusted is used as the evaluation object. Constraint boundaries are adjusted based on the overall evaluation results and used as the conditions for determining iterative termination. The resulting rail alignments are then evaluated to obtain the optimal rail alignment set that significantly improves passenger ride comfort. Finally, the optimal adjustment real number solution is obtained based on the smoothness condition. In the second stage, the step adjustment method uses the optimal adjustment real number solution as the basis for optimizing the step differential integer multiples. The optimal adjustment step differential integer solution is obtained based on the principle of minimizing the two-stage state loss. The present invention effectively controls the unevenness of variable wavelength and fixed wavelength, and formulates an optimal real-number adjustment scheme that takes into account passenger riding comfort in the smoothness optimization control process of solution, evaluation, iterative correction, and re-evaluation. The optimal real-number adjustment amount is converted into an optimal differential integer adjustment amount taking into account the fastener material difference, further effectively improving the unevenness of the rail state, significantly reducing the vibration and shaking phenomena, and obtaining a rail fine-tuning optimization scheme suitable for general engineering conditions.

[0004] The technical solutions of the present invention are as follows:

[0005] A two-stage optimization method for rail state control comprises the following steps:

[0006] S1: The length of the rail to be optimized is segmented into first-stage segments according to a first preset length;

[0007] S2: Establishing a rail state optimization model within a segment length interval of a stage, wherein the segment length interval of a stage is a basic planning unit of a stage;

[0008] S3: Based on the typical sensitive wavelength irregularity function and the rail condition evaluation function, additional adjustment limits for the sleeper fasteners are set, and constraint boundaries corresponding to the adjustment limits, typical sensitive wavelength irregularity, and condition evaluation are set. The constraint boundaries are limit differences, and an inequality constraint model for one-stage rail condition optimization is established.

[0009] S4: Optimize and solve the objective function of the adjustment amount and the inequality constraint model in the first-stage rail state optimization model, and calculate the real number solution of the sleeper fastener adjustment amount. If there is no solution in the current optimization calculation, the corresponding adjustment amount is set to zero;

[0010] S5: Process the rails in each segment length interval according to S2-S4 until the processing of the rails to be optimized is completed, and the state of the adjusted rails is evaluated to obtain an evaluation value of the rail state;

[0011] S6: Evaluate the state of the rail after adjustment obtained by the processing of S1-S5, and adjust the constraint boundary value according to the preset correction step size, use the adjusted constraint boundary value as the constraint boundary value of the inequality constraint model in the next solution, and perform iteration termination condition judgment, wherein the iteration termination condition includes: if the evaluation value of the state of the rail obtained by the current solution is less than the evaluation value of the state of the rail obtained by the previous solution and is less than a threshold, then terminate the iteration;

[0012] S7: Repeat S1-S6 until the iterative correction is terminated;

[0013] S8: After the iteration is terminated, the state of the rail obtained from each solution is judged, and the set of rail states represented by the better state evaluation value is selected. The optimal rail shape and position are selected according to the smoothing information to obtain the optimal real number solution of the rail smoothness state;

[0014] S9: segmenting the length of the rail to be optimized into segments in the second stage according to a second preset length;

[0015] S10: Based on the optimal real number solution, a rail state optimization model within a two-stage segment length interval is established, wherein the two-stage segment length interval is a two-stage basic planning unit;

[0016] S11: Based on the n-order difference function of the residual deviation of the neighborhood points, the waveform consistency function, the limit of the adjustment amount of the sleeper fasteners and the constraint boundary value, an inequality constraint model for the two-stage rail state optimization is established;

[0017] S12: Solve the objective function and inequality constraint model of the second stage by integer programming to obtain the sleeper fastener adjustment amount that is an integer multiple of the fastener material difference. If there is no solution in the current optimization calculation, the corresponding adjustment amount is set to zero.

[0018] S13: Process the rails within each segment length interval according to S10-S12 until the processing of the rails to be optimized is completed, and the optimal differential integer solution for rail adjustment is obtained.

[0019] Preferably, in step S1, the first preset length is greater than or equal to the longest reference chord length used in the rail state optimization model.

[0020] Preferably, in step S1, the first stage segmentation is segmentation moved according to a first preset overlapping interval.

[0021] Preferably, in step S1, the first preset overlapping interval is a first overlapping length of adjacent basic planning units.

[0022] Preferably, in step S1, the first overlapping length is greater than or equal to the length of one sleeper interval.

[0023] Preferably, in step S2, the rail state optimization model within the one-stage segment length interval includes an objective function of the amount to be adjusted of all sleeper fasteners within the interval, a typical sensitive wavelength irregularity function and a rail state evaluation function.

[0024] Preferably, in step S3, the rail condition evaluation function is one or more of internal and external track geometric parameters, deviation difference, and deviation change rate.

[0025] Preferably, in step S3, the sensitive wavelength is determined by the natural frequency of the vehicle body and the running speed of the train, and the typical sensitive wavelength is one or more wavelengths with the most serious unevenness among the sensitive wavelengths.

[0026] Preferably, the adjustment object of the track is a reference rail and / or a non-reference rail.

[0027] Preferably, the inequality constraint model includes:

[0028] When the track to be adjusted is a reference rail, the types of the inequality constraint model include height / track irregularity constraints of a typical sensitive wavelength, and one or more constraints selected from vertical / lateral deviation, height / track irregularity of conventional 30m chord check / 300m chord check / 10m chord verse / 20m chord verse, fastener adjustment amount, deviation difference, and deviation change rate.

[0029] When the track to be adjusted is a non-reference rail and the reference rail state cannot be used as an adjustment reference, the types of inequality constraint models include height / track irregularity constraints of typical sensitive wavelengths, and one or more constraints selected from vertical / lateral deviation, height / track irregularity of conventional 30m chord check / 300m chord check / 10m chord verse / 20m chord verse, fastener adjustment amount, deviation difference, and deviation change rate.

[0030] When the track to be adjusted is a non-reference rail and the reference rail state can be used as an adjustment reference, the types of the inequality constraint model include height / track irregularity constraints of typical sensitive wavelengths, and one or more constraints selected from the group consisting of vertical / lateral deviation, height / track irregularity of conventional 30m chord check / 300m chord check / 10m chord verse / 20m chord verse, fastener adjustment amount, deviation difference, deviation change rate, level / track gauge, and twist / track gauge change rate.

[0031] When the track adjustment object is a double track, the reference track can be used as the adjustment object first, and then the non-reference track can be used as the adjustment object to establish a constraint model; or the non-reference track can be used as the adjustment object first, and then the reference track can be used as the adjustment object to establish a constraint model; or both can be adjusted simultaneously;

[0032] When adjusting simultaneously, the types of the inequality constraint models include one or more constraints of height / track irregularity constraints of a typical sensitive wavelength of the left track, and vertical / lateral deviation of the left track, height / track irregularity of the conventional 30m chord check / 300m chord check / 10m chord verse / 20m chord verse of the left track, amount of left rail fasteners to be adjusted, poor left track deviation, and rate of change of left track deviation; and height / track irregularity constraints of a typical sensitive wavelength of the right track, and one or more constraints of vertical / lateral deviation of the right track, height / track irregularity of the conventional 30m chord check / 300m chord check / 10m chord verse / 20m chord verse of the right track, amount of right rail fasteners to be adjusted, poor right track deviation, and rate of change of right track deviation; and one or more constraints of level / gauge and twist / gauge change rate.

[0033] Preferably, when the inequality constraint model is a height / track constraint, the versine difference constraint is incorporated into the height / track constraint.

[0034] Preferably, in step S3, when the inequality constraint model is first established, the inequality constraint boundary value does not exceed the limit value required by the corresponding current specification.

[0035] Preferably, in step S5, each segment length interval is a segment interval moved according to a first preset overlapping interval.

[0036] Preferably, in step S6, the preset correction step size adjustment constraint boundary value calculation process includes: if the solution of the rail to be optimized is completed for the previous i times, the correction step size of the constraint boundary value used in the i+1th solution is the constraint boundary value used in the i-th solution. times, that is, the constraint limit values ​​of various inequality constraint models used in the i+1th solution are the constraint limit values ​​used when the solution is first solved. times; and so on, determine the constraint limit value of the inequality constraint model in the next iterative calculation.

[0037] Preferably, in step S6, the constraint limit value of the certain type, the constraint limit value used in the i-th solution is:

[0038] (1)

[0039] Where: θ' is the constraint limit value of the i-th time; θ is the constraint limit value when it is first solvable.

[0040] Preferably, in step S6, the evaluation value of the rail state is a function value of mean statistics of statistical results of typical sensitive wavelength irregularities and track geometric state parameters.

[0041] Preferably, the track geometry parameters include one or more of deviation, height / track direction, deviation difference, deviation change rate, level / track gauge, and twist / track gauge change rate.

[0042] Preferably, the statistical results include one or more of the maximum value, minimum value, mean value, and mean error of each parameter.

[0043] Preferably, the mean statistics of the statistical results include one or more of the mean of the maximum values, the mean of the minimum values, the mean of the means, and the mean of the mean errors of each parameter.

[0044] Preferably, in step S6, the threshold is 0.1.

[0045] Preferably, in step S8, the set of rail states is the adjusted rail shape and position represented by a state evaluation value of a combination of optimal, optimal and suboptimal, optimal and suboptimal, and suboptimal.

[0046] Preferably, in step S8, the smoothing information includes one or more of the deviation difference and the deviation change rate of the track geometric state parameters.

[0047] Preferably, in step S9, the second preset length is greater than or equal to the length of the neighborhood point residual deviation n-order difference function and the waveform consistency function used in the rail state optimization model.

[0048] Preferably, in step S9, the second stage segmentation is segmentation moved according to a second preset overlapping interval.

[0049] Preferably, in step S9, the second preset overlapping interval is a second overlapping length of adjacent basic planning units.

[0050] Preferably, in step S9, the second overlapping length is greater than or equal to the length of one sleeper interval.

[0051] Preferably, in step S10, the rail state optimization model within the two-stage segment length interval includes an objective function of the amount to be adjusted of all sleeper fasteners within the interval, an nth-order difference function of the residual deviation of the neighborhood points, and a waveform consistency function.

[0052] Preferably, in step S10, the amount to be adjusted of the rail state optimization model within the two-stage segment length interval is an integer multiple of the step difference.

[0053] Preferably, in step S10, the step difference is one of the specifications of the rail fastener adjustment material, namely, 0.5 mm, 1.0 mm, 1.5 mm, and 2.0 mm.

[0054] Preferably, in step S11, the n-th order difference function of the residual deviation of the neighborhood points is a recursive formula:

[0055] (2)

[0056] The recursive formula can be obtained by the following formula:

[0057] (3)

[0058] Where, Number the sleepers of the rails to be optimized. , is a natural number, , m is the number of sleepers contained in the rail to be optimized, ,and .

[0059] Preferably, in step S11, the waveform consistency function is:

[0060] (4)

[0061] Where, For the difference, is the number of level differences at point i, is the second-stage adjustment quantity at point i and the corresponding optimal real number solution for the first stage The worse.

[0062] Compared with the prior art, the present invention has the following advantages:

[0063] The present invention addresses the problem of insufficient control of the general fixed-wavelength unevenness index in the current track precision measurement and fine-tuning specifications, as well as the problem of uneven effects of differential adjustment schemes caused by the use of low-precision differential adjustment materials in general projects. A two-stage optimization method for rail state control is proposed. The present invention uses a two-stage optimization method to obtain a fastener material differential integer multiple adjustment scheme that ensures high track smoothness. By considering the vibration of the running train and the comfort of passengers, the sensitive wavelength that causes train resonance is controlled as a key factor, more accurately ensuring the smoothness of high-speed operation of the train under complex operating conditions, and obtaining the optimal adjustment amount real number solution to achieve this state. Based on the adjustment line corresponding to the optimal adjustment amount real number solution, integer programming is implemented using the nth-order difference function of the residual deviation of the neighborhood point and the waveform consistency function to obtain a differential integer solution with the minimum loss of the two-stage state, ensuring that the track smoothness obtained in the second stage is consistent with or closest to the track smoothness obtained in the first stage. The present invention can scientifically and accurately formulate a track optimization plan that conforms to the actual fastener material differential adjustment and obtain the optimized track high smoothness in the track state corresponding to the integral multiple adjustment amount of the fastener material differential. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0065] Figure 1 This is a schematic diagram of the overall solution flow of an embodiment of the present invention;

[0066] Figure 2 This is a flow chart of the first stage optimization method in an embodiment of the present invention;

[0067] Figure 3 It is a rail state optimization model within a segment length interval in a first stage in an embodiment of the present invention;

[0068] Figure 4 This is a flow chart of the second stage optimization method in an embodiment of the present invention;

[0069] Figure 5 This is a rail state optimization model within a two-stage segment length interval in an embodiment of the present invention. DETAILED DESCRIPTION

[0070] The present invention is further described below with reference to the accompanying drawings and embodiments. It should be noted that, in the absence of conflict, the embodiments in this application and the technical features in the embodiments can be combined with each other. Unless otherwise defined, the technical terms or scientific terms used in the present invention should be the common meanings understood by people with ordinary skills in the field to which the present invention belongs. The words "including" or "comprising" and the like used in the present invention mean that the elements or objects appearing before the word cover the elements or objects listed after the word and their equivalents, without excluding other elements or objects.

[0071] like Figure 1-5 As shown, a two-stage optimization method for rail state control can be used to adjust the reference rail alone or the non-reference rail alone, or to adjust the reference rail first and then the non-reference rail, or to adjust the non-reference rail first and then the reference rail, or to adjust both rails simultaneously. The method includes the following steps:

[0072] S1: The length of the rail to be optimized is segmented in a first stage according to a first preset length. The first preset length is greater than or equal to the longest reference chord length used in the rail condition optimization model. The first stage segmentation is performed by moving the segments according to a first preset overlapping interval. The first preset overlapping interval is the first overlapping length of adjacent basic planning units, and the first overlapping length is greater than or equal to the length of one sleeper interval.

[0073] S2: Establish a rail state optimization model within a one-stage segment length interval, wherein the one-stage segment length interval is a one-stage basic planning unit, and the rail state optimization model within the one-stage segment length interval includes an objective function of the amount to be adjusted of all sleeper fasteners within the interval, a typical sensitive wavelength irregularity function, and a rail state evaluation function. The objective function can be to minimize the total amount to be adjusted of all sleeper fasteners in the segment planning unit, or minimize the sum of the absolute values ​​of the amounts to be adjusted, or minimize the sum of the squares of the amounts to be adjusted. The sensitive wavelength is determined by the natural frequency of the vehicle body and the running speed of the train. The typical sensitive wavelength is one or more wavelengths with the most serious irregularity among the sensitive wavelengths. The state evaluation function is one or more of the internal and external geometric parameters of the track, poor deviation, and deviation change rate.

[0074] The sensitive wavelength irregularity is the track / height irregularity of the variable wavelength. The sensitive wavelength irregularity function is the track / height irregularity function of the variable wavelength.

[0075] In a specific embodiment, a typical sensitive wavelength determination method is as follows:

[0076] (1) Determine the sensitive wavelength by the natural frequency of the vehicle body and the train running speed:

[0077] (5)

[0078] Where, Sensitive wavelengths determined for different speeds, ; is the running speed of the train, ; is the natural frequency of the vehicle body.

[0079] (2) Evaluate the uneven state of the sensitive wavelengths and select one or several sensitive wavelengths with the most serious state as typical sensitive wavelengths.

[0080] (3) The track direction and height irregularities of the determined typical sensitive wavelengths are incorporated into the track state optimization model.

[0081] In specific embodiments, the number of typical sensitive wavelengths may be one, two, or three. The train's operating speed is determined based on the specific train speed regulations and requirements for the railway line. The natural frequency of the car body is determined by the car body used and is generally within the range of 0.7 to 1.4 Hz.

[0082] The internal and external geometric parameters of the track include one or more of vertical deviation, lateral deviation, height, track direction, level, gauge, twist, and gauge change rate.

[0083] The height / track irregularity in the track internal and external geometric parameters refers to the track irregularity / height irregularity of a certain wavelength.

[0084] In a specific embodiment, the rail condition evaluation function includes track internal and external geometric parameters, deviation difference, and deviation change rate. The track internal and external geometric parameters include vertical deviation, lateral deviation, height irregularity of 10m chord, 20m chord, 5m / 30m chord, and 150m / 300m chord, track direction irregularity of 10m chord, 20m chord, 5m / 30m chord, and 150m / 300m chord, level, gauge, twist, and gauge change rate. The evaluation function corresponding to each parameter is as follows:

[0085] 1) Vertical (or lateral) deviation

[0086] (6)

[0087] Where: is the original deviation; The amount to be adjusted.

[0088] 2) Uneven height (or track direction)

[0089] (7)

[0090] Where: and are the deviations after adjustment of the head and tail points of the reference chord respectively; and They are the deviations after adjustment of the first and last points of the detection string; ,in, 、 are the serial numbers of the first and last points of the reference chord respectively; ,in, 、 are the serial numbers of the first and last points of the detection chord respectively; w is the number of sleepers included in the detection chord length; .

[0091] When using 5m / 30m chord calibration, ; When using 150m / 300m chord calibration, .

[0092] Incorporating the verse difference constraint into the elevation / track irregularity constraint, when using 10m chord or 20m chord verse, the above formula is simplified to:

[0093] (8)

[0094] 3) Level (or track gauge)

[0095] (9)

[0096] Where: and are the adjusted deviations of the two tracks, where For the left (or right) track Point-adjusted deviation, For the right (or left) track The deviation after point adjustment can be calculated by formula (6).

[0097] 4) Twist (or gauge change rate)

[0098] (10)

[0099] Where n is the number of sleepers corresponding to the action distance. The static laying of ballastless track requires a distortion action distance of 3m and a gauge change action distance of 0.625m. r represents the calculation parameter for distortion or gauge change, r=1 (or r=625).

[0100] The evaluation function with poor deviation is as follows:

[0101] (11)

[0102] Where: .

[0103] The evaluation function of the deviation change rate is as follows:

[0104] (12)

[0105] Where: d is the mileage difference between points i and j.

[0106] S3: Based on the typical sensitive wavelength irregularity function and rail condition evaluation function, additional adjustment limits for the sleeper fasteners are set, and constraint boundaries corresponding to the adjustment limits, typical sensitive wavelength irregularities, and condition evaluation are set. The constraint boundaries are limit differences, and an inequality constraint model for one-stage rail condition optimization is established. The sleeper fastener adjustment limit function is as follows:

[0107] (13)

[0108] When setting the constraint limit value for the first time, the assigned value should not exceed the tolerance limit required by the current specification. For example, the height (or track direction) inequality constraint of a 10m chord can be described as:

[0109] (14)

[0110] Where: and It is the limit difference value of height (or track direction) irregularity, that is, the constraint boundary value of the state inequality constraint model.

[0111] In a specific embodiment, if the reference rail is the only adjustment object, the types of inequality constraint models include height (or track direction) irregularity constraints of typical sensitive wavelengths, as well as ① vertical (or lateral) deviation and / or ② 30m chord calibration and / or 300m chord calibration and / or other fixed chord length (wavelength) calibration and / or 10m chord verse and / or 20m chord verse and / or other fixed chord length (wavelength) verses height (or track direction) irregularity and / or ③ fastener adjustment amount and / or ④ deviation difference and / or ⑤ deviation change rate constraint.

[0112] If the non-reference rail is used as the adjustment object alone, when the reference rail state cannot be used as an adjustment reference, the types of inequality constraint models include the height (or track direction) irregularity constraint of the typical sensitive wavelength, and ① vertical (or lateral) deviation and / or ② 30m chord calibration and / or 300m chord calibration and / or other fixed chord length (wavelength) calibration and / or 10m chord verse and / or 20m chord verse and / or other fixed chord length (wavelength) verse height (or track direction) irregularity and / or ③ fastener adjustment amount and / or ④ deviation difference and / or ⑤ deviation change rate constraint; when the reference rail state is not suitable for adjustment, the inequality constraint model shall be used as an adjustment object. The state can be used as a reference for adjustment. The types of inequality constraint models include height (or track direction) irregularity constraints of typical sensitive wavelengths, as well as ① vertical (or lateral) deviation and / or ② 30m chord calibration and / or 300m chord calibration and / or other fixed chord length (wavelength) calibration and / or 10m chord verse and / or 20m chord verse and / or other fixed chord length (wavelength) verses height (or track direction) irregularity and / or ③ fastener adjustment amount and / or ④ deviation difference and / or ⑤ deviation change rate and / or ⑥ level (or track gauge) and / or ⑦ twist (or track gauge change rate) constraints.

[0113] If two rails (one of which is the reference rail and the other is the non-reference rail) are used as the adjustment objects, the reference rail can be used as the adjustment object first according to the above method, and then the non-reference rail can be used as the adjustment object; or the non-reference rail can be used as the adjustment object, and then the reference rail can be used as the adjustment object; or both the reference rail and the non-reference rail can be used as the adjustment objects. In this case, the types of inequality constraint models include reference rail: height (or track direction) irregularity constraint of typical sensitive wavelength, and ① vertical (or lateral) deviation and / or ② 30m chord calibration and / or 300m chord calibration and / or other fixed chord length (wavelength) calibration and / or 10m chord verse and / or 20m chord verse and / or other fixed Height (or track direction) irregularity of chord length (wavelength) verses and / or ③ amount of fastener adjustment to be made and / or ④ deviation difference and / or ⑤ rate of deviation change; Non-reference rail: Height (or track direction) irregularity constraints of typical sensitive wavelengths, as well as ① vertical (or lateral) deviation and / or ② 30m chord calibration and / or 300m chord calibration and / or other fixed (wavelength) chord length calibration and / or 10m chord verses and / or 20m chord verses and / or height (or track direction) of other fixed (wavelength) chord length verses and / or ③ amount of fastener adjustment to be made and / or ④ deviation difference and / or ⑤ rate of deviation change and / or ⑥ level (or track gauge) and / or ⑦ distortion (or track gauge change rate) constraints.

[0114] S4: A mathematical programming method is used to optimize and solve the objective function and inequality constraint model of the first stage. The mathematical programming method may be a simplex method, a dual simplex method, an interior point method, a genetic algorithm, or a simulated annealing algorithm.

[0115] If there is no solution in the current optimization calculation, the corresponding adjustment amount will be set to zero.

[0116] S5: Process the rails in each segment length interval according to S2-S4 until the processing of the rails to be optimized is completed. The segment length intervals are segment intervals that are moved according to the first preset overlapping interval.

[0117] In a specific embodiment, the first preset overlapping interval may be equal to the length of one sleeper interval, or equal to the detection chord length of the longest reference chord used in the rail condition optimization model.

[0118] S6: Evaluate the state of the adjusted rail obtained by processing S1-S5, and adjust the constraint boundary value according to the preset correction step size, use the adjusted constraint boundary value as the constraint boundary value of the inequality constraint model in the next solution, and perform iteration termination condition judgment.

[0119] The preset correction step size adjustment constraint boundary value calculation process includes: if the solution of the rail to be optimized is completed in the previous i times, the correction step size of the constraint boundary value used in the i+1th solution is the constraint boundary value used in the i-th solution. times, that is, the constraint limit values ​​of various inequality constraint models used in the i+1th solution are the constraint limit values ​​used when the solution is first solved. times; and so on, determine the constraint limit value of the inequality constraint model in the next iterative calculation.

[0120] In a specific embodiment, the track irregularity constraint limit value of the 30m chord check is solved for the i-th time as follows:

[0121] (15)

[0122] Where: θ' is the constraint limit value of the i-th time; θ is the constraint limit value when it is first solvable.

[0123] The initial constraint boundary values ​​of different types of inequality constraint models, such as the height irregularity of 30m chord calibration, the track irregularity of 300m chord calibration, and the height irregularity of 300m chord calibration, may be the same or different, and the values ​​are determined based on actual conditions.

[0124] The iteration termination condition includes: terminating the iteration if the difference between the evaluation value of the rail state obtained by the current solution and the evaluation value of the rail state obtained by the previous solution is less than a threshold. The evaluation value of the rail state is a function value of the mean statistics of the statistical results of the typical sensitive wavelength irregularity and the track geometric state parameters.

[0125] In a specific embodiment, the rail condition evaluation values ​​include height (or track-direction) irregularities at a typical sensitive wavelength, as well as ① vertical (or lateral) deviation, and / or ② 30m chord calibration, / or 300m chord calibration, / or calibrations of other fixed chord lengths (wavelengths), and / or height (or track-direction) irregularities of 10m chord verse, / or 20m chord verse, and / or verses of other fixed chord lengths (wavelengths), and / or ③ deviation difference, and / or ④ deviation change rate, and / or ⑤ horizontal (or track gauge), and / or ⑥ twist (or track gauge change rate). The statistical results include ① maximum value, and / or ② minimum value, and / or ③ mean value, and / or ④ mean error of the aforementioned parameters. The mean statistics of the statistical results include ① mean of the maximum value, and / or ② mean of the minimum value, and / or ③ mean of the mean value, and / or ④ mean error of the aforementioned statistical results. The function value of the mean statistic is a single mean statistic, or one or more of the mean, maximum, minimum, and root mean square error of multiple mean statistics, or a poor mean statistic, or a product of poor mean statistics. The poor evaluation value is the absolute value of the poor.

[0126] In a specific embodiment, the state of the entire rail to be adjusted obtained after the i-th iterative solution is evaluated, such as the typical sensitive wavelength, 30m chord check, 300m chord check, 10m chord verse, 20m chord verse height (or track direction) irregularity and deviation change rate, a total of 6 parameters, and the maximum value, minimum value and mean error of the evaluation results of each parameter are statistically analyzed. Then, the average of the maximum value, minimum value and mean error is calculated to obtain the state evaluation value. :

[0127] (16)

[0128] Where: y a 、y b 、y c 、y d 、y e and y f These are the evaluation result vectors of each of the six parameters in the segmented planning unit, namely, typical sensitive wavelength, 30m chord check, 300m chord check, 10m chord verse, 20m chord verse altitude (or track direction) irregularity and deviation change rate; max, min, rmse are the maximum, minimum and mean error calculation functions, respectively.

[0129] In other specific embodiments, Can be:

[0130] (17)

[0131] or:

[0132] (18)

[0133] or:

[0134] (19)

[0135] Where: mean is the mean calculation function.

[0136] or:

[0137] (20)

[0138] Similarly, the rail status obtained by the iterative solution of the i+1th iteration is evaluated similarly to obtain the evaluation value If the absolute value of the difference between the two evaluation values ​​is less than the threshold value, which is 0.1, the iteration is stopped, otherwise the iterative calculation is continued.

[0139] In another specific embodiment, other thresholds may be set according to optimization requirements.

[0140] S7: Repeat S1-S6 until the iterative correction is terminated.

[0141] S8: After the iteration is terminated, the state of the rail obtained from each solution is judged, and the set of rail states represented by the better state evaluation value is selected. The optimal rail shape and position are selected according to the smoothing information to obtain the optimal real number solution of the rail smoothness state.

[0142] In a specific embodiment, the determination is the mean of the statistical results of the track geometric state parameters. The rail state set is the adjusted rail shape and position represented by the state evaluation value of ① optimal, ② optimal and suboptimal, or ③ optimal, suboptimal, and suboptimal. The smoothing information includes ① deviation difference and / or ② deviation change rate. The method is the statistical result of the smoothing information, and the statistical result is one or more of the following: maximum value, minimum value, mean value, and mean square error.

[0143] In a specific embodiment, if the iteration ends at the i-th time, the evaluation value of the rail state obtained in each iteration is , select the optimal and suboptimal evaluation values ​​from the 1-i rail shape and position and , then calculate the deviation difference and deviation change rate of the adjusted rail shape and position obtained at the pth and qth iterations. Statistically compare the maximum, minimum, and mean errors of the deviation difference and deviation change rate of the adjusted rail shape and position obtained at the pth and qth iterations, and take the rail shape and position represented by the smaller one as the optimal rail shape and position, thus obtaining the optimal real number solution.

[0144] S9: The length of the rail to be optimized is segmented in the second stage according to a second preset length. The second preset length is greater than or equal to the length in the neighborhood point residual deviation n-order difference function and the waveform consistency function used in the rail state optimization model. The second stage segmentation is segmented according to a second preset overlapping interval. The second preset overlapping interval is the second overlapping length of adjacent basic planning units, and the second overlapping length is greater than or equal to the length of one sleeper interval.

[0145] S10: Based on the optimal real number solution, a rail state optimization model within a two-stage segment length interval is established, wherein the two-stage segment length interval is a two-stage basic planning unit, and the rail state optimization model within the two-stage segment length interval includes the objective function of the amount to be adjusted of all sleeper fasteners within the interval, the nth-order difference function of the residual deviation of the neighborhood points, and the waveform consistency function.

[0146] The amount to be adjusted in the rail state optimization model within the two-stage segment length interval is an integer multiple of the step difference. The step difference is a specification of the rail fastener adjustment material of one of 0.5mm, 1.0mm, 1.5mm and 2.0mm.

[0147] The objective function of the rail state optimization model within the two-stage segment length interval is to minimize the cumulative sum of the differences between the two-stage adjusted quantities and the corresponding one-stage optimal real number solution, or to minimize the sum of the absolute values ​​of the differences, or to minimize the sum of the squares of the differences.

[0148] The n-order difference function of the residual deviation of the neighborhood point is a recursive formula:

[0149] (twenty one)

[0150] The recursive formula can be obtained by the following formula:

[0151] (twenty two)

[0152] Where: Number the sleepers of the rails to be optimized. , is a natural number, , m is the number of sleepers contained in the rail to be optimized, ,and .

[0153] In the n-th order difference function, n does not exceed the number of sleepers contained in the rail to be optimized minus 1.

[0154] In a specific embodiment, , When , the nth-order difference function of the residual deviation of the neighborhood points is simplified to the difference between the residual deviation difference between the first point and the second point and the residual deviation difference between the second point and the third point in the three adjacent intervals.

[0155] The waveform consistency function is:

[0156] (twenty three)

[0157] Where, For the difference, is the number of level differences at point i, is the second-stage adjustment quantity at point i and the corresponding optimal real number solution for the first stage The worse.

[0158] S11: Based on the nth-order difference function of the residual deviation of the neighborhood points, the waveform consistency function, the limit of the adjustment amount of the sleeper fasteners, and the constraint boundary, an inequality constraint model for the two-stage rail state optimization is established.

[0159] The inequality constraint of the n-order difference function of the residual deviation of the neighborhood point can be described as:

[0160] (twenty four)

[0161] Where, is the limit difference value of the n-order difference function of the residual deviation of the neighborhood point, that is, the constraint limit value of the inequality constraint model, .

[0162] In a specific embodiment, the limit difference is:

[0163] (25)

[0164] Where, is the rate of change, l is the number of sleeper intervals, ,and , where m is the number of sleepers contained in the rail to be optimized.

[0165] In a specific embodiment, when , hour, ,and , is a positive real number.

[0166] The inequality constraints of the waveform consistency function can be described as:

[0167] (26)

[0168] The limit on the amount of adjustment to be made for the sleeper fasteners is the same as that in the first stage.

[0169] S12: Solve the objective function and inequality constraint model in the second stage using an integer programming method. The integer programming method may employ a branch and bound method, a cutting plane method, an implicit enumeration method, a Hungarian method, or a Monte Carlo method. After solving the problem, the sleeper fastener adjustment values ​​for integer multiples of the fastener material difference are obtained.

[0170] If there is no solution in the current optimization calculation, the corresponding adjustment amount will be set to zero.

[0171] S13: Process the rails within each segment length interval according to S10-S12 until the processing of the rails to be optimized is completed, and the optimal differential integer solution for rail adjustment is obtained.

[0172] The segment length intervals are segment intervals that are moved according to a second preset overlapping interval.

[0173] In a specific embodiment, the second preset overlapping interval may be equal to the length of one sleeper interval, or equal to the length of the nth-order difference function of the neighborhood point residual deviation and the waveform consistency function used in the rail state optimization model.

[0174] The above description is merely a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any technician familiar with the present profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. A two-stage optimization method for rail state control, characterized in that: The following steps are involved: S1: The length of the rail to be optimized is segmented into first-stage segments according to a first preset length; S2: establishing a rail state optimization model within a one-stage segment length interval, wherein the one-stage segment length interval is a one-stage basic planning unit, and the rail state optimization model within the one-stage segment length interval includes an objective function of the amount to be adjusted of all sleeper fasteners within the interval, a typical sensitive wavelength irregularity function, and a rail state evaluation function; S3: Based on the typical sensitive wavelength irregularity function, the state evaluation function, the limit of the amount of adjustment to be made for the sleeper fasteners, and the constraint boundary value, an inequality constraint model for one-stage rail state optimization is established; S4: Optimize and solve the objective function and inequality constraint model of the first stage to obtain the real number solution of the sleeper fastener adjustment amount; S5: Process the rails in each segment length interval according to S2-S4 until the rails to be optimized are processed, and evaluate the state of the adjusted rails to obtain an evaluation value of the rail state; S6: Adjust the constraint value, repeat S1-S5, and determine whether to terminate the iteration based on the evaluation value; S7: If it is not terminated, repeat S6 until the iteration is terminated; S8: After the iteration is terminated, the state of the rail obtained by each iteration is judged, the set of rail states represented by the better state evaluation value is selected, and the optimal rail shape and position are selected according to the smoothing information to obtain the optimal real number solution of the rail smoothness state; S9: segmenting the length of the rail to be optimized into segments in the second stage according to a second preset length; S10: Based on the optimal real number solution, a rail state optimization model within a two-stage segment length interval is established. The two-stage segment length interval is a two-stage basic planning unit. The rail state optimization model within the two-stage segment length interval includes an objective function of the amount to be adjusted for all sleeper fasteners within the interval, an n-order difference function of the residual deviation of the neighborhood point, and a waveform consistency function. The amount to be adjusted for the rail state optimization model within the two-stage segment length interval is an integer multiple of the level difference, and the n-order difference function of the residual deviation of the neighborhood point is a recursive formula , the recursive formula is given by Get, among them, Number the sleepers of the rails to be optimized. , is a natural number, , m is the number of sleepers contained in the rail to be optimized, l is the number of sleeper intervals, ,and , the waveform consistency function is ,in, For the difference, is the number of level differences at point i, is the second-stage adjustment quantity at point i and the corresponding optimal real number solution for the first stage The poor; S11: Based on the nth-order difference function of the residual deviation of the neighborhood points, the waveform consistency function, the limit of the adjustment amount of the sleeper fasteners and the constraint boundary value, an inequality constraint model for the two-stage rail state optimization is established; S12: Solve the objective function and inequality constraint model of the second stage by integer programming to obtain the adjustment amount of the sleeper fastener that is an integer multiple of the fastener material difference; S13: Process the rails within each segment length interval according to S10-S12 until the processing of the rails to be optimized is completed, and the optimal differential integer solution for rail adjustment is obtained.

2. A two-stage optimization method for rail state control according to claim 1, characterized in that: In step S1, the first preset length is greater than or equal to the longest reference chord length used in the rail state optimization model, the first stage segmentation is to move the segmentation according to the first preset overlapping interval, the first preset overlapping interval is the first overlapping length of adjacent basic planning units, and the first overlapping length is greater than or equal to the length of one sleeper interval.

3. The two-stage optimization method for rail state control according to claim 1, characterized in that: In step S2, the rail condition evaluation function is one or more of internal and external geometric parameters of the track, deviation difference, and deviation change rate.

4. A two-stage optimization method for rail state control according to claim 1, characterized in that: In step S3, the sensitive wavelength is determined by the natural frequency of the vehicle body and the running speed of the train, and the typical sensitive wavelength is one or more wavelengths with the most serious unevenness among the sensitive wavelengths.

5. The two-stage optimization method for rail state control according to claim 1, characterized in that: In step S3, the inequality constraint model includes: When the track to be adjusted is the reference rail, the types of the inequality constraint model include height / track irregularity constraints of typical sensitive wavelengths, and one or more constraints selected from the group consisting of vertical / lateral deviation, height / track irregularity of conventional 30m chord check / 300m chord check / 10m chord verse / 20m chord verse, fastener adjustment amount, deviation difference, and deviation change rate. When the track to be adjusted is not the reference rail and the reference rail state cannot be used as an adjustment reference, the types of inequality constraint models include height / track irregularity constraints of typical sensitive wavelengths, as well as one or more constraints selected from the group consisting of vertical / lateral deviation, height / track irregularity of conventional 30m chord check / 300m chord check / 10m chord verse / 20m chord verse, fastener adjustment amount, deviation difference, and deviation change rate. When the track to be adjusted is a non-reference rail and the reference rail state can be used as an adjustment reference, the types of inequality constraint models include height / track irregularity constraints of typical sensitive wavelengths, and one or more of the following constraints: vertical / lateral deviation, height / track irregularity of conventional 30m chord check / 300m chord check / 10m chord verse / 20m chord verse, fastener adjustment amount, deviation difference, deviation change rate, level / track gauge, and twist / track gauge change rate. When the track adjustment object is two tracks, the reference track can be used as the adjustment object first, and then the non-reference track can be used as the adjustment object to establish a constraint model; or the non-reference track can be used as the adjustment object first, and then the reference track can be used as the adjustment object to establish a constraint model; or both can be adjusted simultaneously; When adjusting simultaneously, the type of the inequality constraint model includes one or more constraints of height / track irregularity of a typical sensitive wavelength of the left track, vertical / lateral deviation of the left track, height / track irregularity of conventional 30m chord check / 300m chord check / 10m chord verse / 20m chord verse of the left track, amount of left rail fasteners to be adjusted, poor left track deviation, and rate of change of left track deviation; and height / track irregularity constraint of a typical sensitive wavelength of the right track, vertical / lateral deviation of the right track, height / track irregularity of conventional 30m chord check / 300m chord check / 10m chord verse / 20m chord verse of the right track, amount of right rail fasteners to be adjusted, poor right track deviation, and rate of change of right track deviation; and one or more constraints of level / gauge and twist / gauge change rate; When the inequality constraint model is a height / track constraint, the versine difference constraint is incorporated into the height / track constraint.

6. A two-stage optimization method for rail state control according to claim 1, characterized in that: In step S5, the evaluation value of the rail condition is a function value of the mean statistics of the statistical results of the typical sensitive wavelength irregularity and the track geometric state parameters, the track geometric state parameters include one or more of deviation, height / track direction, deviation difference, deviation change rate, level / track gauge, and twist / track gauge change rate, the statistical results include one or more of the maximum value, minimum value, mean, and mean error of each parameter, and the mean statistics of the statistical results include one or more of the mean of the maximum value, the mean of the minimum value, the mean of the mean, and the mean error of the mean of each parameter.

7. A two-stage optimization method for rail state control according to claim 1, characterized in that: In step S6, the calculation process of adjusting the constraint limit value includes: if the solution of the rail to be optimized is completed in the previous i times, the correction step length of the constraint limit value used in the i+1th solution is the constraint limit value used in the i-th solution. times, that is, the constraint limit values ​​of various inequality constraint models used in the i+1th solution are the constraint limit values ​​used when the solution is first solved. times; and so on, determine the constraint limit value of the inequality constraint model in the next iterative calculation.

8. The two-stage optimization method for rail state control according to claim 1, characterized in that: In step S8, the set of rail states is the adjusted rail shape and position represented by a state evaluation value of a combination of optimal, optimal and suboptimal, optimal and suboptimal, and suboptimal, and the smoothing information includes one or more of deviation difference and deviation change rate.

9. The two-stage optimization method for rail state control according to claim 1, characterized in that: In step S9, the second preset length is greater than or equal to the length of the nth-order difference function of the residual deviation of the neighborhood points and the waveform consistency function used in the rail state optimization model, the second stage segmentation is to move the segmentation according to the second preset overlapping interval, the second preset overlapping interval is the second overlapping length of adjacent basic planning units, and the second overlapping length is greater than or equal to the length of one sleeper interval.

10. The two-stage optimization method for rail state control according to claim 1, characterized in that: In step S10, the step difference is one of the specifications of the rail fastener adjustment material, 0.5 mm, 1.0 mm, 1.5 mm, and 2.0 mm.

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