Optimal matching design method for track beam-rail integration for multi-level vibration reduction

Abstract

The present invention relates to the field of rail vehicle technology, and more specifically, to a method for designing an optimal rail-beam integration for multi-level vibration reduction. The method comprises the following steps: Step 1: deriving a coupled design equation for multiple vibration reduction levels of a train track system; Step 2: decoupling the coupled design equation for multiple vibration reduction levels; Step 3: using Taylor expansion to expand the functions corresponding to different parameters to the nth order for fitting; and Step 4: solving the equation for each level with multiple unknown optimal parameters using a neural network. The present invention can preferably obtain design parameters.

Description

Technical Field

[0001] The present invention relates to the technical field of rail vehicles, and in particular to a design method for optimal matching of rail-beam integration for multi-level vibration reduction. Background Art

[0002] In recent years, urban rail transit systems have been developing rapidly. However, with the construction of urban rail and inter-city high-speed railways, railway lines will inevitably get closer and closer to schools, hospitals, residential areas, and facilities that require shock absorption. The vibration and noise problems caused by this have caused great trouble to surrounding residents, facilities, and passengers.

[0003] To this end, various vibration reduction methods have been proposed in recent years. First, the two-layer vibration reduction structure of rail-track bearing plate-foundation is targeted. Since the vibration reduction of the rail-track bearing plate vibration reduction layer and the track bearing plate-foundation vibration reduction layer is relatively simple and there are relatively few adjustable contents, there is still room for optimization and improvement of the vibration reduction effect. Therefore, it is necessary to study the vibration reduction of three-layer and higher-level tracks. However, due to the mutual coupling between the parameters of the multi-level vibration reduction layers and the high dimensionality, it is extremely difficult to obtain the optimal solution. Therefore, it is necessary to design a track beam integrated optimal matching design method for multi-level vibration reduction to obtain the design parameters. Summary of the Invention

[0004] The present invention provides a method for designing an optimal matching of rail-beam integration for multi-level vibration reduction, which can better obtain design parameters.

[0005] The track beam-rail integrated optimal matching design method for multi-level vibration reduction according to the present invention comprises the following steps:

[0006] Step 1: Derive the coupled design equations for the multiple vibration reduction levels of the train-track system;

[0007] Step 2: Decouple the coupled design equations of multiple vibration reduction levels;

[0008] Step 3: Through Taylor expansion, expand the functions corresponding to different parameters to nth order for fitting;

[0009] Step 4: There are multiple unknown optimal parameters in the equation for each level, which are solved using a neural network.

[0010] Preferably, in step 1, the details are as follows:

[0011] The train track system consists of three layers of vibration reduction, from top to bottom: rails, fasteners or elastic vibration-damping filling materials, rail beams, vibration-damping pads, bridge supports, vibration-damping layers, and base plates. The fasteners or elastic vibration-damping filling materials, vibration-damping pads, and vibration-damping layers act as damping springs, while the base plate is rigid.

[0012] The coupling design formula for multiple vibration reduction levels is:

[0013] A=f(x1,x2,…,x n ) (1)

[0014] where x1 to x n For different vibration reduction levels, x1 is the first level vibration reduction, which is a fastener or elastic vibration reduction filling material, x2 is the second level vibration reduction, which is a vibration reduction pad, and x3 is the third level vibration reduction, which is a vibration reduction layer; A is the vibration acceleration Z level.

[0015] Preferably, in step 2, specifically:

[0016] The original equation (1) is a linear equation in which parameters at all levels are coupled to each other, including a second-order strong coupling term:

[0017] Πx i x j (i≠j) (2)

[0018] And multi-order weak coupling terms:

[0019] Πx i x j ....x n (i≠j≠....≠n) (3)

[0020] x i , x j , x n is a hierarchical variable;

[0021] The linear equation is converted into a nonlinear independent equation and the vibration reduction parameters at each level are solved iteratively and independently to obtain the decoupled equation:

[0022] A=f(x1)f(x2)f(x3)....f(x n ) (4)

[0023] Although the decoupled equations become nonlinear, the optimal solution of the decoupled design equations for multiple vibration reduction levels can be deduced by simply finding the optimal design for the corresponding equations at different levels.

[0024] Preferably, in step 3, specifically:

[0025] Through Taylor expansion, the functions corresponding to different parameters are expanded to nth order for fitting; for a layer of function f(x n ) is expanded to obtain:

[0026]

[0027] o(n) is a high-order error term, and a, b, c, and d are unknown optimal parameters. By retaining the low-order terms and ignoring the high-order terms, a simplified approximate equation is obtained while ensuring engineering accuracy. The above function is obtained for each layer of the three-layer vibration reduction design.

[0028] Preferably, in step 4, specifically:

[0029] There are multiple unknown optimal parameters in each layer of the equation, namely a, b, c, and d, so they are solved through a neural network. First, a neural network model suitable for regression tasks is constructed. The 2.5D finite element boundary element calculation results are used as input layer parameters, and are passed layer by layer. Each layer contains several neurons, and after using a nonlinear activation function, the mapping relationship with the true function is finally approximated. The performance of the model is then evaluated through cross-validation to ensure that the model can accurately fit the unknowns. After the model training is completed, the predictions and estimates of the unknowns a, b, c, and d are finally output. These predicted values ​​are substituted into the original equation to observe the optimization results.

[0030] The present invention can provide a design idea for obtaining optimal design parameters for three-layer and higher-level vibration reduction structures, thereby further completing the vibration reduction design and reducing the impact of track noise and vibration on the surrounding environment and passengers. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 This is a flow chart of a method for designing optimal track beam-rail integration for multi-level vibration reduction in an embodiment;

[0032] Figure 2 Schematic diagram of a track coupling model using a three-layer vibration reduction structure of rail-rail beam-bridge support-base plate in the embodiment;

[0033] Figure 3 Schematic diagram of a parameter fitting neural network model suitable for regression tasks in an embodiment. DETAILED DESCRIPTION

[0034] In order to further understand the content of the present invention, the present invention is described in detail with reference to the accompanying drawings and embodiments. It should be understood that the embodiments are merely for explaining the present invention and are not intended to limit the present invention.

[0035] Example

[0036] like Figure 1 As shown, this embodiment provides a method for designing an optimal matching of rail-beam integration for multi-level vibration reduction, which includes the following steps:

[0037] Step 1: Derive the coupled design equations for the multiple vibration reduction levels of the train-track system;

[0038] Step 2: Decouple the coupled design equations of multiple vibration reduction levels;

[0039] Step 3: Through Taylor expansion, expand the functions corresponding to different parameters to nth order for fitting;

[0040] Step 4: There are multiple unknown optimal parameters in the equation for each level, which are solved using a neural network.

[0041] In step 1, the details are as follows:

[0042] like Figure 2 As shown in the figure, the train track system consists of rails, fasteners or elastic vibration-damping filling materials, rail beams, vibration-damping pads, bridge supports, vibration-damping layers, and base plates from top to bottom, with three layers of vibration reduction. The fasteners or elastic vibration-damping filling materials, vibration-damping pads, and vibration-damping layers are damping springs, and the base plate is rigid.

[0043] The coupling design formula for multiple vibration reduction levels is:

[0044] A=f(x1,x2,…,x n ) (1)

[0045] where x1 to x n For different vibration reduction levels, x1 is the first-level vibration reduction, which is a fastener or elastic vibration-damping filling material, that is, the part directly connected to the rail. If it is a fastener-type track system, it is a fastener system; if it is an embedded track, it is an elastic vibration-damping filling material; x2 is the second-level vibration reduction, which is a vibration-damping pad; x3 is the third-level vibration reduction, which is a vibration-damping layer; A is the vibration acceleration Z level.

[0046] In step 2, specifically:

[0047] The original equation (1) is a linear equation in which parameters at all levels are coupled to each other, including a second-order strong coupling term:

[0048] Πx i x j (i≠j) (2)

[0049] And multi-order weak coupling terms:

[0050] Πx i x j ....x n (i≠j≠....≠n) (3)

[0051] x i , x j , x n is a hierarchical variable;

[0052] The problem of rapidly increasing complexity will occur during the solution process, making it difficult to match the design. Therefore, the linear equation is converted into a nonlinear independent equation and the vibration reduction parameters at each level are solved iteratively and independently to obtain the decoupled equation:

[0053] A=f(x1)f(x2)f(x3)....f(x n ) (4)

[0054] Although the decoupled equations become nonlinear, the optimal solution of the decoupled design equations for multiple vibration reduction levels can be deduced by simply finding the optimal design for the corresponding equations at different levels.

[0055] In step 3, specifically:

[0056] By Taylor expansion, the functions corresponding to different parameters are expanded to nth order for fitting; expanding one layer of function yields:

[0057]

[0058] o(n) is a high-order error term, and a, b, c, and d are unknown optimal parameters. By retaining the low-order terms and ignoring the high-order terms, a simplified approximate equation is obtained while ensuring engineering accuracy. The above function is obtained for each layer of the three-layer vibration reduction design.

[0059] In step 4, specifically:

[0060] There are multiple unknown optimal parameters in each level of the equation, namely a, b, c, d, so they are solved by neural network. Taking the fitting neural network as an example, Figure 3 As shown in the figure, a neural network model suitable for regression tasks is first constructed; the 2.5D finite element boundary element calculation results are used as input layer parameters, and are passed layer by layer. Each layer contains several neurons, and a nonlinear activation function (including ReLU or Sigmoid) is used to finally approximate the mapping relationship with the true function; the performance of the model is then evaluated by the cross-validation method to ensure that the model can accurately fit the unknowns; after the model training is completed, the predictions and estimates of the unknowns a, b, c, and d are finally output; these predicted values ​​are substituted into the original equation to observe the optimization results.

[0061] This embodiment can provide a design approach for obtaining optimal design parameters for vibration reduction structures at three layers and above, thereby further completing the vibration reduction design and reducing the impact of track noise and vibration on the surrounding environment and passengers.

[0062] The above is a schematic description of the present invention and its embodiments, which is not restrictive. The drawings show only one embodiment of the present invention, and the actual structure is not limited thereto. Therefore, if a person skilled in the art is inspired by this and, without departing from the purpose of the present invention, designs a structure and embodiment similar to this technical solution without inventiveness, they shall fall within the scope of protection of the present invention.

Claims

1. A design method for optimal track beam-rail integration for multi-level vibration reduction, characterized by: The following steps are involved: Step 1: Derive the coupled design equations for the multiple vibration reduction levels of the train-track system; In step 1, the details are as follows: The train track system consists of three layers of vibration reduction, from top to bottom: rails, fasteners or elastic vibration-damping filling materials, rail beams, vibration-damping pads, bridge supports, vibration-damping layers, and base plates. The fasteners or elastic vibration-damping filling materials, vibration-damping pads, and vibration-damping layers act as damping springs, while the base plate is rigid. The coupling design formula for multiple vibration reduction levels is: A=f(x1,x2,…,x n ) (1) where x1 to x n represents different vibration reduction levels, x1 represents the first level of vibration reduction, which is a fastener or elastic vibration reduction filling material, x2 represents the second level of vibration reduction, which is a vibration reduction pad, and x3 represents the third level of vibration reduction, which is a vibration reduction layer; A represents the vibration acceleration Z level; Step 2: Decouple the coupled design equations of multiple vibration reduction levels; In step 2, specifically: The original equation (1) is a linear equation in which parameters at all levels are coupled to each other, including a second-order strong coupling term: Πx i x j (i≠j) (2) And multi-order weak coupling terms: Πx i x j ....x n (i≠j≠....≠n) (3) x i , x j , x n is a hierarchical variable; The linear equation is converted into a nonlinear independent equation and the vibration reduction parameters at each level are solved iteratively and independently to obtain the decoupled equation: A=f(x1)f(x2)f(x3)....f(x n ) (4) Although the decoupled equations become nonlinear, the optimal solution of the decoupled design equations for multiple vibration reduction levels can be deduced by simply finding the optimal design for the corresponding equations at different levels. Step 3: Use Taylor expansion to expand the functions corresponding to different parameters to nth order for fitting; In step 3, specifically: Through Taylor expansion, the functions corresponding to different parameters are expanded to nth order for fitting; for a layer of function f(x n ) is expanded to obtain: o(n) is a high-order error term, and a, b, c, and d are unknown optimal parameters. The low-order terms are retained and the high-order terms are ignored, resulting in a simplified approximate equation while ensuring engineering accuracy. The above function is obtained for each layer of the three-layer vibration reduction design. Step 4: There are multiple unknown optimal parameters for each layer in the equation, namely a, b, c, and d, so they are solved through a neural network. First, a neural network model suitable for regression tasks is constructed. The 2.5D finite element boundary element calculation results are used as input layer parameters, and are passed layer by layer. Each layer contains several neurons, and after using a nonlinear activation function, the mapping relationship with the true function is finally approximated. The performance of the model is then evaluated through cross-validation to ensure that the model can accurately fit the unknowns. After the model training is completed, the predictions and estimates of the unknowns a, b, c, and d are finally output. These predicted values ​​are substituted into the original equation to observe the optimization results.

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