Multi-objective Optimization Design Method of High-Speed Railway Catenary Based on FNN and NSGA-II

Abstract

The present invention discloses a multi-objective optimization design method for the pantograph-catenary system of high-speed railways based on FNN and NSGA-II, specifically as follows: constructing a pantograph-catenary coupling model, taking the minimum of the standard deviation of the contact force and the maximum uplift at the positioning point as the optimization objectives, determining the optimization range of the catenary parameters by comparing the existing catenary parameter ranges and the material properties of each wire, and establishing an optimization model; sampling through Latin hypercube design to obtain the initial samples of the design parameters, calculating the standard deviation of the contact force and the maximum uplift at the positioning point of the initial sample points by using numerical simulation methods, establishing an FNN approximation model, and then using the NSGA-II algorithm to find the optimal solution in the design space to optimize the design of the catenary; verifying the optimization results and outputting the optimal values and the corresponding combinations of design parameters. The present invention greatly improves the calculation efficiency of the pantograph-catenary coupling and the optimization efficiency; and at the same time considering multiple design parameters, makes the optimization results of the catenary have global and universal applicability.

Description

Technical Field

[0001] The invention belongs to the field of high-speed railway catenary systems, and in particular relates to a multi-objective optimization design method for high-speed railway catenary systems based on FNN and NSGA-II. Background Art

[0002] Overhead contact network, commonly referred to as catenary, is a system that provides electric energy to electric railway vehicles through sliding contact with the pantograph. The interaction force between the pantograph and the contact network determines the current collection quality [1]. As the train speed increases, the contact network vibrates more and the contact force fluctuates more violently, resulting in a serious deterioration in the current collection quality of the pantograph and the catenary. In order to improve the current collection quality, many scholars have conducted relevant research on the design parameters of the contact network and optimized the design of the contact network on this basis.

[0003] Poetsch and Finner[2] proposed a catenary method based on the finite difference method, using two-dimensional Euler-Bernoulli beam elements to equivalent contact wires and load-bearing cables. Based on this method, Cho et al.[3,4] established a contact network model and introduced a pantograph concentrated mass model to analyze the effects of contact network pre-sag and hanger strings on the current collection of the pantograph. Carnicero and Lopez-Garcia[5] applied a nonlinear finite element method to establish a contact network model and analyzed the effects of the pantograph-cattograph contact model on the results. Zhang Jian et al.[6] discussed the changes in contact force when the design parameters of the contact network changed. By introducing the Spearman correlation coefficient, the relationship between the changes in design parameters and the contact force was analyzed.

[0004] Gregori et al. [7] used genetic algorithms to optimize the contact wire height and the spatial arrangement of the suspension strings to improve the current collection quality. The above methods directly seek the optimal solution for the traditional bow-net coupling model, which is computationally intensive and inefficient. The optimization of the contact network only considers the standard deviation of the contact force and considers few parameters, which is not comprehensive enough.

[0005] Su Kaixin et al. [8] used a combination of back propagation neural network (BPNN) and genetic algorithm to optimize the current-receiving mass, which improved the computational efficiency. However, they did not optimize multiple design parameters at the same time and only considered a single optimization indicator, namely the standard deviation of the contact force, which has limitations.

[0006] Wang et al. [9] used the average contact force deviation and the contact force standard deviation as optimization indicators. However, due to the complexity of the pantograph-catenary coupling system, directly optimizing the pantograph-catenary coupling finite element model has a large amount of calculation and low computational efficiency.

[0007] Therefore, the existing contact network optimization design method cannot take into account multiple design parameters and select multiple optimization indicators while having high computational efficiency. In summary, a new method is urgently needed to solve this problem.

[0008] References:

[0009] [1] Liu Zhigang, Song Yang, Han Ye, et al. Research Progress of High-Speed Railway Overhead Contact Lines [J]. Journal of Southwest Jiaotong University, 2016, 51(03): 495-518.

[0010] [2] FINNER L, POETSCH G, SARNES B, et al. Program for Catenary-Pantograph Analysis, PrOSA Statement of Methods and Validation according EN 50318 [J]. Vehicle System Dynamics, 2015, 53(3): 305-313.

[0011] [3] CHO Y H. Numerical Simulation of the Dynamic Responses of Railway Overhead Contact Lines to a Moving Pantograph, Considering a Nonlinear Dropper [J]. Journal of Sound and Vibration, 2008, 315(3): 433-454.

[0012] [4] CHO Y H, LEE K, PARK Y, et al. Influence of Contact Wire Pre-sag on the Dynamics of Pantograph-Railway Catenary [J]. International Journal of Mechanical Sciences, 2010, 52(11): 1471-1490.

[0013] [5] LOPEZ-GARCIA O, CARNICERO A, TORRES V. Computation of the Initial Equilibrium of Railway Overheads Based on the Catenary Equation [J]. Engineering Structures, 2006, 28(10): 1387-1394.

[0014] [6]ZHANG J,LIU W,ZHANG Z.Sensitivity analysis and research onoptimisation methods of design parameters of high-speed railway catenary[J].IET ELECTRICAL SYSTEMS IN TRANSPORTATION,2019,9(3):150-156.

[0015] [7]GREGORI S,TUR M,NADAL E,et al.An approach to geometricoptimisation of railway catenaries[J].VEHICLE SYSTEM DYNAMICS,2018,56(8):1162-1186.

[0016] [8]SU K,ZHANG J,ZHANG J,et al.Optimisation of current collectionquality of high-speed pantograph-catenary system using the combination ofartificial neural network and genetic algorithm[J].VEHICLE SYSTEM DYNAMICS,2023,61(1):260-285.

[0017] [9]WANG H,ZHENG D,HUANG P,et al.Design optimisation of railwaypantograph-catenary systems with multiple objectives[J].VEHICLE SYSTEMDYNAMICS,2022。 Summary of the Invention

[0018] In view of the above technical problems, the present invention provides a multi-objective optimal design method for high-speed railway catenary based on FNN and NSGA-II.

[0019] A multi-objective optimal design method for high-speed railway catenary based on FNN and NSGA-II of the present invention comprises the following steps:

[0020] Step 1: Construct a pantograph-catenary coupling model. A catenary model is established using non-linear cable-bar elements, and the pantograph adopts a three-mass model. The coupling between the pantograph and the catenary uses the penalty function, and the accuracy of the model is verified using the EN50318-2018 standard.

[0021] Step 2: Taking the minimum of the standard deviation of the contact force STD and the maximum uplift of the positioning point MUS as the optimization objectives, the contact wire tension t1, the carrier cable tension t2, the elastic sling tension t3, and the distances d1, d2, d3 between each dropper and the left positioning rod are used as optimization parameters. By comparing the existing catenary parameter ranges and the material properties of each wire, the catenary parameter optimization range is determined, and an optimization model is established. The optimization model is as follows:

[0022]

[0023] where f1 and f2 are the objective functions corresponding to STD and MUS respectively, t i and d i represent the design variables, t min , t max , d min , d max represent the upper and lower limits of the corresponding design variables respectively.

[0024] Step 3: Use Latin hypercube sampling to select parameter combinations. Design parameter combinations are obtained through Latin hypercube sampling within the parameter ranges selected in Step 2.

[0025] Step 4: Construct a training sample set. Substitute the design parameter combinations obtained in Step 3 into the pantograph-catenary coupling model established in Step 1 respectively, and extract the standard deviation of the contact force and the maximum uplift of the positioning point corresponding to each design parameter combination to form a sample set.

[0026] Step 5: Establish an FNN neural network approximation model based on the input-output relationship of the initial samples, and then allocate the training set and the test set according to a certain proportion.

[0027] Step 6: Train the FNN approximation model. Use the training set samples obtained in Step 5 to train the FNN approximation model and adjust the number of hidden layer nodes.

[0028] Step 7: Test the prediction accuracy of the FNN approximation model. Use the test set samples obtained in Step 5 to test the accuracy of the FNN approximation model trained in Step 6. If the accuracy requirement is not met, return to Step 6. If the accuracy requirement is met, proceed to the next step.

[0029] Step 8: Select NSGA-II parameters. Select the number of iterations, the population size, the number of objective functions, and the dimensional parameters.

[0030] Step 9: Use NSGA-II for optimization. Apply the NSGA-II algorithm after selecting the parameters in Step 8 to solve the FNN approximation model established in Step 7, solve the multi-objective optimization Pareto front, and extract the minimum values of the standard deviation of the contact force and the maximum lift of the positioning point of the objective function, as well as the corresponding optimal design parameter combinations.

[0031] Step 10: Verify the optimization result. Substitute the optimal design parameter combination solved in Step 9 into the pantograph-catenary coupling model established in Step 1, and verify the error between the minimum values of the standard deviation of the contact force and the maximum lift of the positioning point of the optimization objective function and the calculation results of the pantograph-catenary coupling model. If the error meets the requirements, output the optimal value and the corresponding design parameter combination.

[0032] Further, in Step 5, the training set is 90% and the test set is 10%.

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

[0034] The present invention applies an FNN neural network approximation model to replace the traditional pantograph-catenary coupling model. Compared with the existing methods, the calculation amount is greatly reduced, and the calculation efficiency of the pantograph-catenary coupling is greatly improved.

[0035] The present invention combines the genetic algorithm with the approximation model to optimize the design of the catenary. The NSGA-II algorithm is used to optimize and calculate the FNN approximation model, which greatly improves the optimization efficiency.

[0036] The present invention adopts a multi-objective optimization design for the catenary, and simultaneously considers various design parameters, making the optimization result of the catenary have global and universal applicability. Description of the Drawings

[0037] Figure 1 It is a flow chart of the multi-objective optimization design method for high-speed railway catenary based on FNN and NSGA-II of the present invention.

[0038] Figure 2 It is a schematic diagram of the pantograph-catenary coupling model established by MATLAB.

[0039] Figure 3 It is an optimization flow chart based on the FNN approximation model.

[0040] Figure 4 It is a schematic diagram of the Pareto front solved by the NASA-II algorithm. Detailed Embodiment

[0041] The following further illustrates the content of the present invention in conjunction with the drawings and embodiments.

[0042] The flow of a multi-objective optimization design method for high-speed railway catenary based on FNN and NSGA-II of the present invention is as Figure 1As shown in the figure, it specifically includes the following steps:

[0043] Step 1: Construct a pantograph-catenary coupling model. As shown in the figure, a non-linear cable-bar element is used to establish the catenary model, the pantograph adopts a three-mass model, the coupling between the pantograph and the catenary uses a penalty function, and the accuracy of the model is verified by the EN50318-2018 standard. Figure 2 As shown in the figure, a non-linear cable-bar element is used to establish the catenary model, the pantograph adopts a three-mass model, the coupling between the pantograph and the catenary uses a penalty function, and the accuracy of the model is verified by the EN50318-2018 standard.

[0044] Step 2: Taking the minimum of the standard deviation STD of the contact force and the maximum uplift MUS of the positioning point as the optimization objective, the contact wire tension t1, the carrier cable tension t2, the elastic sling tension t3, and the distances d1, d2, d3 between each dropper and the left positioning rod as the optimization parameters. By comparing the existing catenary parameter ranges and the material properties of each wire, determine the optimization range of the catenary parameters and establish an optimization model. The optimization model is:

[0045]

[0046] where f1 and f2 are the objective functions corresponding to STD and MUS respectively, t i and d i represent the design variables, and t min , t max , d min , d max represent the upper and lower limits of the corresponding design variables respectively.

[0047] Step 3: Use Latin hypercube sampling to select parameter combinations. Obtain the design parameter combinations through Latin hypercube sampling within the parameter ranges selected in Step 2.

[0048] Step 4: Construct a training sample set. Substitute the design parameter combinations obtained in Step 3 into the pantograph-catenary coupling model established in Step 1 respectively, and extract the standard deviation of the contact force and the maximum uplift of the positioning point corresponding to each design parameter combination to form a sample set.

[0049] Step 5: Establish an FNN neural network approximation model based on the input-output relationship of the initial samples, and then allocate the training set (90%) and the test set (10%) according to a certain proportion.

[0050] Step 6: Train the FNN approximation model. Use the training set samples obtained in Step 5 to train the FNN approximation model and adjust the number of hidden layer nodes.

[0051] Step 7: Test the prediction accuracy of the FNN approximation model. Use the test set samples obtained in Step 5 to test the accuracy of the FNN approximation model trained in Step 6. If the accuracy requirement is not met, return to Step 6; if the accuracy requirement is met, proceed to the next step.

[0052] Step 8: Select the NSGA-II parameters, including the number of iterations, population size, number of objective functions, and dimensional parameters.

[0053] Step 9: Use NSGA-II for optimization. Apply the NSGA-II algorithm with the parameters selected in Step 8 to solve the FNN approximation model established in Step 7, solve the multi-objective optimization Pareto front, and extract the minimum values of the standard deviation of the contact force and the maximum lifting amount of the positioning point in the objective function, as well as the corresponding optimal design parameter combinations.

[0054] Step 10: Verify the optimization results. Substitute the optimal design parameter combination obtained in Step 9 into the pantograph-catenary coupling model established in Step 1, and verify the error between the minimum values of the standard deviation of the contact force and the maximum lifting amount of the positioning point in the optimization objective function and the calculation results of the pantograph-catenary coupling model. If the error meets the requirements, output the optimal value and the corresponding design parameter combination.

[0055] Example:

[0056] In this example, the basic parameters of the catenary and pantograph are as follows: the catenary span is 60 m, the tensions of the contact wire, carrier cable, and elastic suspension are 37 kN, 24 kN, and 3.5 kN respectively, the number of droppers is 6, and the initial distances from the left side are 4 m, 14 m, and 24 m respectively. The DSA380 pantograph is selected, and the operating speed is 400 km / h.

[0057] In the example, the parameter optimization ranges determined in Step 2 are as follows:

[0058] 35 kN ≤ t1 ≤ 39 kN

[0059] 20 kN ≤ t2 ≤ 28 kN

[0060] 2.5 kN ≤ t3 ≤ 4.5 kN

[0061] 3 m ≤ d1 ≤ 5 m

[0062] 13 m ≤ d2 ≤ 15 m

[0063] 23 m ≤ d3 ≤ 25 m

[0064] Based on the optimization model established in Step 2, take the standard deviation of the contact force STD and the maximum lifting amount of the positioning point MUS as the objective functions, and take the tensions t1, t2, t3 of the contact wire, carrier cable, and elastic suspension, and the distances d1, d2, d3 between each dropper and the left positioning rod as the design variables to determine the design space. Sample through Latin hypercube design and obtain the initial samples of the design parameters. Use the numerical simulation method to calculate the standard deviation of the contact force and the maximum lifting amount of the positioning point at the initial sample points. After establishing the FNN approximation model, use the NSGA-II algorithm to find the optimal solution in the design space and optimize the design of the catenary. The optimization process is as Figure 3As shown, output the values of the objective function and each design variable corresponding to the Pareto front results to a file, and extract the objective function values in the output file to form the Pareto front, such as Figure 4 As shown.

[0065] The optimal solution obtained when the maximum number of generations is reached and the algorithm converges, that is, the tensions of the contact wire, the catenary wire, and the elastic messenger wire are 38.982 kN, 27.427 kN, and 2.560 kN respectively, the distances of the three droppers from the left side are 6.994 m, 14.966 m, and 24.080 m respectively, the standard deviation of the contact force is 32.914 N, and the maximum uplift at the positioning point is 101.5 mm. Compare the analysis results of the structures before and after optimization. Under the same operating conditions, the standard deviation of the contact force is reduced by 19.63%, and the maximum uplift at the positioning point is reduced by 17.54%.

Claims

1. A multi-objective optimization design method for high-speed railway catenary based on FNN and NSGA-II, characterized in that, It includes the following steps: Step 1: Construct a pantograph-catenary coupling model. A catenary model is established using non-linear cable-bar elements, the pantograph adopts a three-mass model, and the coupling between the pantograph and the catenary uses the penalty function. The accuracy of the model is verified using the EN50318-2018 standard; Step 2: With the minimum of the standard deviation of the contact force STD and the maximum uplift of the positioning point MUS as the optimization objectives, the catenary tension t1, the carrier cable tension t2, the elastic sling tension t3, and the distances d1, d2, d3 between each dropper and the left positioning rod are used as optimization parameters. By comparing the existing catenary parameter ranges and the material properties of each wire, the catenary parameter optimization range is determined, and an optimization model is established. The optimization model is: Among them, f1 and f2 are the objective functions corresponding to STD and MUS respectively, t i and d i represent design variables, t min , t max , d min , d max represent the upper and lower limits of the corresponding design variables respectively; Step 3: Use Latin hypercube sampling to select parameter combinations, and obtain design parameter combinations through Latin hypercube sampling within the ranges of each parameter selected in Step 2; Step 4: Construct a training sample set. Substitute the design parameter combinations obtained in Step 3 into the pantograph-catenary coupling model established in Step 1 respectively, and extract the standard deviation of the contact force and the maximum uplift of the positioning point corresponding to each design parameter combination to form a sample set; Step 5: Establish an FNN neural network approximation model based on the input-output relationship of the initial samples, and then allocate the training set and the test set according to a certain ratio; Step 6: Train the FNN approximation model. Use the training set samples obtained in Step 5 to train the FNN approximation model and adjust the number of hidden layer nodes; Step 7: Test the prediction accuracy of the FNN approximation model. Use the test set samples obtained in Step 5 to test the accuracy of the FNN approximation model trained in Step 6. If the accuracy requirement is not met, return to Step 6. If the accuracy requirement is met, proceed to the next step; Step 8: Select NSGA-II parameters, select the number of iterations, population size, number of objective functions, and dimension parameters; Step 9: Use NSGA-II for optimization. Apply the NSGA-II algorithm after selecting the parameters in Step 8 to solve the FNN approximation model established in Step 7, solve the multi-objective optimization pareto front, and extract the minimum values of the objective functions of the standard deviation of the contact force and the maximum uplift of the positioning point and the corresponding optimal design parameter combinations; Step 10: Verify the optimization results. Substitute the optimal design parameter combinations solved in Step 9 into the pantograph-catenary coupling model established in Step 1, and verify the error between the minimum values of the optimization objective functions of the standard deviation of the contact force and the maximum uplift of the positioning point and the calculation results of the pantograph-catenary coupling model. If the error meets the requirements, output the optimal values and the corresponding design parameter combinations.

2. A multi-objective optimization design method for high-speed railway catenary based on FNN and NSGA-II according to claim 1, characterized in that, In Step 5, the training set is 90% and the test set is 10%.

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