High-speed railway track fine-tuning optimization method considering multi-chord constraints

Abstract

The invention discloses a high-speed railway track fine-tuning optimization method considering multi-chord constraints, comprising: establishing constraint conditions of a high-speed railway track fine-tuning model; establishing a model, constructing an objective function of an adjustment node, and deriving an evaluation matrix from original data; obtaining optimized deviation data by generating an adjustment measurement vector and superimposing it with an original deviation; using an iterative algorithm, after generating an adjustment measurement vector and optimizing a line shape, completing the first iteration; for subsequent iterations, using the optimized line shape as input deviation data; then, converting the deviation data into an adjustment space matrix and an evaluation matrix, and recalculating the optimized line shape after the second iteration; the invention can be applied to daily track unevenness operation maintenance, realizing rapid output of a fine-tuning plan, and avoiding the complexity of manual plan generation.

Description

Technical Field

[0001] The invention relates to the technical field of railways and rail transportation, and in particular to a high-speed railway track fine-tuning optimization method considering multi-chord constraints. Background Art

[0002] Track unevenness is an important source of interference for trains and the main cause of vibration and wheel-rail interaction. Track unevenness seriously affects the safety, stability, comfort and service life of vehicles, and is also the main limiting factor for train speed. For the adjustment of ballastless track unevenness, the upper limit of the adjustment amount of the fastener system and various smoothness indicators must be considered. The constraints are relatively complex and difficult to adjust manually. Summary of the invention

[0003] In order to solve the problems existing in the prior art, the purpose of the present invention is to provide a high-speed railway track fine-tuning optimization method considering multi-chord constraints. The present invention can be applied to daily track unevenness maintenance operations to achieve rapid output of fine-tuning solutions and avoid the complexity of manual solution generation.

[0004] To achieve the above object, the technical solution adopted by the present invention is: a high-speed railway track fine-tuning optimization method considering multi-chord constraints, comprising the following steps:

[0005] Step 1: Establish the constraint conditions of the high-speed railway track fine-tuning model;

[0006] Step 2: Model establishment, construct the objective function of the adjustment node, and derive the evaluation matrix from the original data;

[0007] Step 3, obtaining optimized deviation data by generating an adjusted measurement vector and superimposing it with the original deviation;

[0008] Step 4: Using the iterative algorithm, after generating the adjustment measurement vector and optimizing the line shape, the first iteration is completed; for subsequent iterations, the optimized line shape is used as the input deviation data; then, the deviation data is converted into the adjustment space matrix and the evaluation matrix, and the optimized line shape is recalculated after the second iteration.

[0009] As a further improvement of the present invention, in step 1, the constraints include track adjustment space and track smoothness constraints.

[0010] As a further improvement of the present invention, in step 2, the objective function includes the objective function of the adjustment amount of each adjustment node, the midpoint chord measurement objective function and the objective function of the vector distance difference method.

[0011] As a further improvement of the present invention, the objective function of the adjustment amount of each adjustment node is specifically as follows:

[0012]

[0013] Where i is the adjustment node number, a lim is the deviation limit from the design elevation, To adjust the strategy vector, is the objective function corresponding to the adjusted node i.

[0014] As a further improvement of the present invention, the method for constructing the midpoint chord measurement objective function is as follows:

[0015] Calculate the adjusted node as the average value of the middle point, end point and starting point of the detected chord in the chord measurement method:

[0016]

[0017] in, is the average value of the chord measurement when the detection point is at i, c j1 is the detection chord length, p is the absolute deviation data; the changes of the average chord measurement values ​​of the middle point, end point and starting point of the detection chord before and after adjustment are as follows:

[0018]

[0019] in, The corresponding detection chord change after adjusting the i-th node;

[0020] The objective function of the midpoint chord measurement of the i-th adjustment node is the sum of the squares of the average changes in the midpoint chord measurements of the middle point, end point, and starting point of the detection chord before and after adjustment divided by three times the limit, as follows:

[0021]

[0022] As a further improvement of the present invention, the method for constructing the objective function of the vector distance difference method is as follows:

[0023] The adjustment node is calculated as the average value of the end point of the moving chord, the starting point of the moving chord, the end point of the detection chord, and the starting point of the detection chord in the vector distance difference method:

[0024]

[0025] is the average value of the vector distance difference when the detection point is at i. The average values ​​of the end point of the moving chord, the starting point of the moving chord, the end point of the detection chord, and the starting point of the detection chord before and after adjustment are as follows:

[0026]

[0027] The objective function of the vector difference method for the i-th adjustment node To adjust the end point of the moving chord, the starting point of the moving chord, the end point of the detection chord, and the starting point of the detection chord, the sum of the squares of the average value changes is divided by four times the vector distance difference constraint value, as follows:

[0028]

[0029] As a further improvement of the present invention, in step 4, for the calculation of the adjustment evaluation score, the input adjustment amount is the accumulated adjustment amount, and the adjustment space matrix is ​​synchronized and updated after each iteration to ensure that the optimized line shape is within the adjustment space.

[0030] As a further improvement of the present invention, the weights of all objective functions need to satisfy the following conditions:

[0031]

[0032] Among them, w1 is the adjustment amount weight, w2 is the 10m chord weight, w3 is the 60m chord weight, w4 is the 5 / 30m vector distance difference weight, and w5 is the 150 / 300m vector distance difference weight. By increasing the over-limit chord constraint, a feasible weight combination that meets all indicators is output.

[0033] The beneficial effects of the present invention are:

[0034] 1. In order to solve the problems that the existing manual fine-tuning algorithms lack intelligence, the intelligent fine-tuning algorithms have a large amount of calculation and cannot simultaneously fine-tune indicators of each frequency band of unevenness, the present invention proposes a track unevenness intelligent fine-tuning algorithm based on vector calculation and considering multi-chord constraints, which is different from the traditional linear programming method. This method only needs to collect the original deviation data of track unevenness, and by setting the target weights of unevenness evaluation indicators and adjustment amounts, it realizes the automatic output of adjustment plans and ensures a relatively small cumulative adjustment amount. At the same time, this model uses corresponding auxiliary algorithms to make the fine-tuning plan under the output weight combination meet the requirements of track smoothness. This method is practical and can be applied to daily track unevenness operation and maintenance to achieve rapid output of fine-tuning plans and avoid the complexity of manual plan generation;

[0035] 2. The present invention regards the track fine-tuning calculation as a multi-objective optimization problem. The chord measurement method and vector distance difference method corresponding to long and short waves can be used as targets for separate adjustments, while considering the adjustment amplitude of each fastener. Compared with the traditional filtering algorithm, this method can consider the adjustment amplitude of the track fastener system. Compared with the linear programming method, this method reduces the amount of calculation and is easy to apply. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is a flow chart of an embodiment of the present invention;

[0037] Figure 2This is a schematic diagram of the track adjustment section structure in an embodiment of the present invention;

[0038] Figure 3 A schematic diagram of a structure for adjusting a space matrix in an embodiment of the present invention;

[0039] Figure 4 It is a schematic diagram of a structure in which the nodes are adjusted to be the middle point, the end point and the starting point of the detection chord in the chord measurement method in an embodiment of the present invention;

[0040] Figure 5 It is a structural schematic diagram of adjusting nodes to be the end point of the moving chord, the starting point of the moving chord, the end point of the detection chord and the starting point of the detection chord in the vector distance difference method in an embodiment of the present invention;

[0041] Figure 6 A comparison diagram of the adjustment method of an embodiment of the present invention and a manual adjustment solution;

[0042] Figure 7 Schematic diagram of a process for determining an appropriate weight combination in an embodiment of the present invention. DETAILED DESCRIPTION

[0043] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0044] Example

[0045] like Figure 1 As shown, a high-speed railway track fine-tuning optimization method considering multi-chord constraints includes:

[0046] Step 1: Model constraints:

[0047] Step 1.1, track adjustment space:

[0048] For track fine-tuning, the adjustment range of each sleeper is not infinite, it depends on the current state of each sleeper fastener system. Due to the restrictions on the type, quantity and thickness of the track pads, the adjustment space of a single sleeper is discrete and bounded. For WJ-8 fasteners, the pads are composed of kneeling pads and adjustment pads. The influence of the number and thickness of pads on the adjustment space is as follows: Figure 2 As shown. The maximum rail lift includes a 10mm rail pad plus two 8mm adjustment pads, totaling 26mm, and the minimum rail lift includes a 5mm rail pad, totaling 5mm. The difference between the maximum and minimum lifts is 21mm, which is the adjustment range, or it can be called the interpolation of the upper and lower limits of the adjustment.

[0049] For ballastless track, the adjustment amount is a multiple of 0.5 mm, so the adjustment for a single sleeper is finitely discrete, with an interpolation interval of 0.5 mm and a vector size of 43. Each sleeper adjustment vector is combined to form an adjustment space matrix A with a matrix size of 43×N, where N is the number of adjustment nodes (sleepers). Assuming that the upward fine adjustment is positive, Figure 3 Shows how to determine the adjustment space matrix.

[0050] Step 1.2: Track smoothness constraint:

[0051] The following table shows the track smoothness constraints. Although this method focuses on adjusting the vertical roughness, horizontal roughness fine-tuning is also satisfied.

[0052]

[0053] Step 2: Model building:

[0054] Step 2.1, objective function:

[0055] Step 2.1.1, adjustment amount:

[0056] The generated adjustment strategy should minimize the adjustment margin as much as possible. Therefore, the adjustment amount of each adjustment node should be a key indicator. The adjustment amount objective function is as follows:

[0057]

[0058] i is the adjustment node number; a lim It is the deviation limit from the design elevation, which is 10mm; To adjust the strategy vector, is the objective function corresponding to the adjusted node i.

[0059] Step 2.1.2, midpoint chord measurement objective function:

[0060] Analyze the impact of adjusting a single node on the midpoint measurement value. Each node can be the starting point / end point of the detection chord, or the middle point. The adjustment of each node also affects the corresponding chord measurement value. Figure 4 All possibilities are shown, and the table below shows the range of influence of the adjustment node.

[0061] (a) Adjust the node to the middle point of the chord measurement method; (b) Adjust the node to the end point of the detection chord; (c) Adjust the node to the starting point of the detection chord:

[0062]

[0063] In order to reduce the amount of calculation, the average value of the midpoint chord measurement method in the above three cases is calculated as follows:

[0064]

[0065] in, is the average value of the chord measurement when the detection point is at i, c j1 To detect the chord length, p is the absolute deviation data; the changes in the average value of the chord measurement in the above three situations before and after adjustment are as follows:

[0066]

[0067] in, The corresponding detection chord change after adjusting the i-th node;

[0068] The objective function of the chord measurement method for the i-th node is the sum of the squares of the average values ​​of the above three cases divided by three times the limit, as shown below:

[0069]

[0070] Step 2.1.3, vector distance difference method:

[0071] The influence of the vector distance difference method is also analyzed. For its calculation, each node can be used as one of the starting and ending points of the detection string, or as one of the starting and ending points of the moving string in the detection string. The four cases are as follows Figure 5 The corresponding impact range is shown in the following table:

[0072] (a) Adjust the node as the end point of the moving chord; (b) Adjust the node as the starting point of the moving chord; (c) Adjust the node as the end point of the detection chord; (d) Adjust the node as the starting point of the detection chord:

[0073]

[0074] The corresponding average value calculation formula is:

[0075]

[0076] is the average value of the vector distance difference when the detection point is at i, and the average value changes after adjustment:

[0077]

[0078] Objective value function It is the sum of the squares of the average values ​​of the four cases divided by four times the vector difference constraint value.

[0079]

[0080] Step 2.2, optimization algorithm:

[0081] Following the above procedure, the evaluation matrix E can be derived from the original data. Subsequently, by generating an adjusted measurement vector and superimposing it with the original deviation, the optimized deviation data can be obtained. It is worth mentioning that the result may not represent the optimal solution under the current weight combination. As mentioned earlier, the relationship between the adjustment of each node and the indicator is not independent. Specifically, the midpoint chord is affected by three nodes, while the vector difference is affected by four nodes. Therefore, the adjustment made to one node may affect the actual scores of all four indicators associated with the node, resulting in a complex interaction between these factors.

[0082] In order to reduce this effect, an iterative algorithm is designed in this embodiment. After generating the adjustment measurement vector and optimizing the linear shape, the first iteration is completed. For subsequent iterations, the optimized linear shape is used as the input deviation data. Then, the deviation data is converted into an adjustment space matrix and an evaluation matrix, and the optimized linear shape is recalculated after the second iteration. It is important to note that for the calculation of the adjustment evaluation score, the input adjustment amount should be the cumulative adjustment amount, not the adjustment amount of the nth iteration. In addition, the adjustment space matrix needs to be synchronized and updated after each iteration to ensure that the optimized linear shape is within the adjustment space.

[0083] In addition, MSC-FT aims to output the optimal adjustment strategy for a specific mileage segment. However, the process of obtaining the evaluation matrix requires the absolute deviation data of adjacent nodes within a certain range. Some nodes cannot get the corresponding evaluation vector because the calculation requires the absolute deviation data beyond the adjustment range. Therefore, two sequences, whose element values ​​are equal to the deviations of the starting and ending points, are connected to both sides of the original data. Therefore, the evaluation array of the aforementioned node can be calculated. The mileage extension is only for the calculation of the evaluation function. The uneven curve of the subsequent part will not include the extension part.

[0084] Step 2.3: Algorithm for obtaining feasible weight combinations:

[0085] A feasible weight combination means that the adjustment amount is as small as possible while satisfying all the indicators. The weights of all objective functions need to meet the following conditions:

[0086]

[0087] Among them, w1 is the weight of the adjustment amount, w2 is the weight of the 10m chord, w3 is the weight of the 60m chord, w4 is the weight of the 5 / 30m vector difference, and w5 is the weight of the 150 / 300m vector difference. In order to minimize the total adjustment amount, the weight of the adjustment amount needs to be as large as possible, while reducing the weights of other indicators. By increasing the overlimit chord constraint, a feasible weight combination that satisfies all indicators can be output.

[0088] The following uses a ballastless track roadbed arch as an engineering example to verify the scientificity and feasibility of the method of this embodiment. In this example, due to the expansion of the roadbed soil, the track is not smooth and presents an upward curve, which reduces the overall smoothness of the track and greatly increases the difficulty of outputting the fine-tuning solution. Comparing the manual adjustment solution with this invention, as shown in the figure, Figure 6 shown.

[0089] Compared with the manual method, the method of this embodiment has the following advantages:

[0090] 1. The cumulative adjustment amount has been significantly reduced, from 1657.1mm to 703mm, a decrease of about 58%.

[0091] 2. The adjustment interval is also greatly reduced. Manual adjustment requires 370 nodes to be adjusted, but for the method in this paper, only 203 nodes need to be adjusted, a 45% reduction.

[0092] 3. The adjustment plan is more user-friendly. The staff can directly adjust the indicator weight combination to reserve the adjustment space of the fastener, which is convenient for the next adjustment.

[0093] The present embodiment is further described below:

[0094] An embodiment of the present invention provides a method for outputting a track fine-tuning scheme suitable for high-speed railway maintenance. The specific implementation process of the method includes two parts: model calling and obtaining feasible weight combinations.

[0095] Here, a case study of a ballastless railway project is used to demonstrate the effectiveness of the algorithm. In this case, due to the effect of expansive soil, the roadbed deformed upward, resulting in a significant upward bulge in one place, which greatly increased the difficulty of track fine-tuning operations.

[0096] The corresponding adjustment parameters are input into the model, including: absolute track deviation data, upper and lower limits of adjustment corresponding to each fastener system, peak constraints of each indicator, and initial weight combination. After calculation, the adjustment strategy under the initial weight can be generated.

[0097] Since the weights of different variables have different effects on the adjustment plan, in order to generate an appropriate plan with all indicators below the limits, an appropriate combination of weights of the five objectives should be determined. Under the constraints already mentioned, the appropriate combination should minimize the total adjustment. Figure 7 The process used to determine the appropriate weight combination is shown. The increment step size is set to 0.02.

[0098] Figure 7The results show that the intercepts of different filling areas on the y-axis represent the corresponding weights within a cycle. Initially, the 150 / 300 ACO indicator exceeded the 10mm limit, so the adjustment amount and the 150 / 300 ACO weight continued to increase and squeezed the weights of the other three indicators. Figure 7 As shown in (b), the peak value of each indicator changes with the change of weight combination. As the weights of 10m MCO, 60m MCO and 5 / 30ACO decrease, their peak values ​​increase slightly, but they do not exceed the limit in the end. The best weight combination appears at the 98th iteration, which is [0.335, 0.029, 0.029, 0.029, 0.579].

[0099] By statically testing the rail irregularities, the absolute deviation data is output, assuming that the WJ-8 fastening system is used. Since the state of the fastening system of each sleeper is unknown, it is assumed that the track under all nodes has a 10mm shim plus a 0.5mm adjustment pad, a total of 10.5mm. According to the previous section, the adjustment range of all nodes is [-10.5, 10.5], and the adjustment boundaries can be obtained. The measured values ​​and the upper / lower boundaries are in Figure 6 Displayed in.

[0100] from Figure 6 It can be seen that the maximum deviation reaches 20mm. Four evaluation indicators for height unevenness are selected, and the peak values ​​of these indicators are: 1.92mm for 10m string, 5.91mm for 60m string, 5.13mm for 5 / 30, and 19.32mm for 150 / 300 string. Two indicators of the difference in distance are out of limit.

[0101] y = 0 is the design line shape. However, due to the large deviation of height unevenness, it is difficult to adjust to the design line shape. Through testing, the applicability of this method is good.

[0102] For the method of this embodiment, after about 10 iterations, the 150 / 300 vector distance difference meets the smoothness requirement. By sacrificing the weights of other indicators, the cumulative adjustment amount can be further optimized. In 100 iterations, the number of iterations corresponding to the solution with the minimum cumulative adjustment amount is 98.

[0103]

[0104]

[0105] The above-mentioned embodiments only express the specific implementation of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the present invention. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A high-speed railway track fine-tuning optimization method considering multi-chord constraints, characterized in that: The following steps are involved: Step 1: Establish the constraint conditions of the high-speed railway track fine-tuning model; Step 2: Model establishment, construct the objective function of the adjustment node, and derive the evaluation matrix from the original data; the objective function includes the objective function of the adjustment amount of each adjustment node, the midpoint chord measurement objective function and the objective function of the vector distance difference method; the objective function of the adjustment amount of each adjustment node is as follows: Where i is the adjustment node number, a lim is the deviation limit from the design elevation, To adjust the strategy vector, To adjust the objective function corresponding to node i; Step 3, obtaining optimized deviation data by generating an adjusted measurement vector and superimposing it with the original deviation; Step 4: Using the iterative algorithm, after generating the adjustment measurement vector and optimizing the line shape, the first iteration is completed; for subsequent iterations, the optimized line shape is used as the input deviation data; then, the deviation data is converted into the adjustment space matrix and the evaluation matrix, and the optimized line shape is recalculated after the second iteration.

2. The high-speed railway track fine-tuning optimization method considering multi-chord constraints according to claim 1 is characterized in that: In step 1, the constraints include track adjustment space and track smoothness constraints.

3. The high-speed railway track fine-tuning optimization method considering multi-chord constraints according to claim 1 is characterized in that: The construction method of the midpoint chord measurement objective function is as follows: Calculate the adjusted node as the average value of the middle point, end point and starting point of the detected chord in the chord measurement method: in, is the average value of the chord measurement when the detection point is at i, c j1 is the detection chord length, p is the absolute deviation data; the changes of the average chord measurement values ​​of the middle point, end point and starting point of the detection chord before and after adjustment are as follows: in, The corresponding detection chord change after adjusting the i-th node; The objective function of the chord measurement at the midpoint of the i-th adjustment node To adjust the limit of the sum of the squares of the average changes in the midpoint chord measurements of the middle point, end point, and starting point of the front and rear detection chord divided by three times, as follows:

4. The high-speed railway track fine-tuning optimization method considering multi-chord constraints according to claim 3 is characterized in that: The construction method of the objective function of the vector distance difference method is as follows: The adjustment node is calculated as the average value of the end point of the moving chord, the starting point of the moving chord, the end point of the detection chord, and the starting point of the detection chord in the vector distance difference method: The average value of the vector distance difference when the detection point is at i, the average value of the end point of the moving chord, the starting point of the moving chord, the end point of the detection chord and the starting point of the detection chord are adjusted. as follows: The objective function of the vector difference method for the i-th adjustment node To adjust the end point of the moving chord, the starting point of the moving chord, the end point of the detection chord, and the starting point of the detection chord, the sum of the squares of the average value changes is divided by four times the vector distance difference constraint value, as follows:

5. The high-speed railway track fine-tuning optimization method considering multi-chord constraints according to claim 4 is characterized in that: In step 4, for the calculation of the adjustment evaluation score, the input adjustment amount is the accumulated adjustment amount, and the adjustment space matrix is ​​synchronized and updated after each iteration to ensure that the optimized line shape is within the adjustment space.

6. The high-speed railway track fine-tuning optimization method considering multi-chord constraints according to claim 5 is characterized in that: The weights of all objective functions need to satisfy the following conditions: Among them, w1 is the adjustment amount weight, w2 is the 10m chord weight, w3 is the 60m chord weight, w4 is the 5 / 30m vector distance difference weight, and w5 is the 150 / 300m vector distance difference weight. By increasing the over-limit chord constraint, a feasible weight combination that meets all indicators is output.

Images