Vehicle-line-bridge coupled vibration acceleration calculation method based on LSTM algorithm

Abstract

The invention discloses a train-line-bridge coupling vibration acceleration calculation method based on an LSTM algorithm, and belongs to the field of axle coupling calculation acceleration, and the method comprises the steps: building an axle coupling calculation model for solving the dynamic response time history of a bridge and a train based on an axle coupling theory; acquiring a plurality of groups of bridge information, acquiring dynamic response of the bridge by using an axle coupling calculation model, and establishing a corresponding relation data set of initial response and subsequent response of the bridge response; training the LSTM neural network by using the corresponding relation data set of the initial response and the subsequent response of the bridge response to obtain a trained LSTM network; and inputting new bridge information, and directly recurding a subsequent bridge response from the bridge response calculated by the axle coupling calculation model in the preorder time by using the trained LSTM network, thereby completing the acceleration of the axle coupling calculation. According to the method, the problems of time consumption and low efficiency in existing axle coupling calculation are solved.

Description

Technical Field

[0001] The present invention belongs to the field of vehicle-bridge coupling calculation acceleration, and in particular relates to a vehicle-line-bridge coupling vibration acceleration calculation method based on an LSTM algorithm. Background Art

[0002] As China's high-speed railway bridges develop towards structural complexity and flexibility, and the speed of railway trains continues to increase. When a train passes over a bridge, it will first cause deformation and vibration of the bridge, which will directly affect the local dynamic performance and service life of the bridge; on the other hand, the vibration of the bridge will also affect the driving safety and riding comfort of the train when it passes over the bridge, and even cause serious accidents such as train derailment in extreme cases. Therefore, the research on the coupled dynamic calculation of trains and bridges has far-reaching significance for improving the stability and durability of bridge structures and the driving safety and comfort of trains.

[0003] Traditional vehicle-bridge coupling calculation methods mainly rely on finite element analysis (FEA), which is computationally intensive and time-consuming, especially when dealing with complex or large-scale structures. These conventional techniques often have challenges in quickly adapting to the changing conditions of bridges under different loads and environmental influences, and are computationally inefficient.

[0004] An existing technical solution is based on the structural dynamics theory of multi-system coupling, which calculates the dynamic response of bridge vehicles when a train passes through a dual-purpose bridge for road and rail. The method has clear theory and clear results. However, the method involves solving large structural dynamic matrix numerical integration methods, which requires high computer performance and is relatively time-consuming. Summary of the invention

[0005] In view of the above-mentioned deficiencies in the prior art, the present invention provides a vehicle-line-bridge coupling vibration acceleration calculation method based on LSTM algorithm, which solves the problems of time-consuming calculation and low efficiency in the existing vehicle-bridge coupling calculation.

[0006] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is: a vehicle-line-bridge coupled vibration acceleration calculation method based on LSTM algorithm, comprising the following steps:

[0007] S1. Based on the vehicle-bridge coupling theory, a vehicle-bridge coupling calculation model is established to solve the dynamic response time history of bridges and trains;

[0008] S2, obtaining several groups of bridge information, using the vehicle-bridge coupling calculation model to obtain the dynamic response of the bridge, and establishing a corresponding relationship data set between the initial response and the subsequent response of the bridge, wherein the subsequent response is the response after the initial response moment;

[0009] S3, using the data set of the correspondence between the initial response and the subsequent response of the bridge response to train the LSTM neural network, and obtain a trained LSTM network;

[0010] S4. Input new bridge information, and use the trained LSTM network to directly recursively derive subsequent bridge responses from the bridge responses calculated by the vehicle-bridge coupling calculation model at the previous time, thereby accelerating the vehicle-bridge coupling calculation.

[0011] Furthermore, the step S1 is specifically as follows:

[0012] S101. Establish a finite element model for the bridge based on the train-bridge coupling theory, and establish a multi-body dynamics model for the train;

[0013] S102, based on the finite element model and the multi-body dynamics model, the track irregularity is used as an excitation to construct the system motion equation;

[0014] S103, solving the system motion equation in the time domain by a numerical integration method to obtain the dynamic response time history of the bridge and the train;

[0015] S104. Construct a vehicle-bridge coupling calculation model based on steps S101-S103.

[0016] Furthermore, the expression of the system motion equation in step S102 is:

[0017]

[0018]

[0019] F V-B =k wi ×D B

[0020] D Bi =X Bi +r i

[0021] Among them, M V is the mass matrix of the train subsystem; is the acceleration vector of the train subsystem; C V is the damping matrix of the train subsystem; is the speed of the train subsystem; K V is the stiffness matrix of the train subsystem; X V is the displacement of the train subsystem; F V-B and F B-V are the interaction forces between the train and the bridge; M B is the mass matrix of the bridge subsystem; is the acceleration vector of the bridge subsystem; CB is the damping matrix of the bridge subsystem; is the speed of the bridge subsystem; K B is the stiffness matrix of the bridge subsystem; X B is the displacement of the bridge subsystem; k wi is the stiffness of each wheelset of the train; D B The actual position of the bridge space under each wheel; D Bi is the actual position of the i-th node of the bridge; X Bi is the dynamic displacement of the ith node of the bridge subsystem; r i is the unevenness value at the bridge node i.

[0022] Furthermore, the integral expression of the numerical integration method in step S103 is:

[0023]

[0024] Among them, X n+1 is the displacement of the n+1th integration step; Δt is the time integration step; α and β are both integration parameters; is the acceleration vector of the n+1th integration step; is the velocity of the n+1th integration step.

[0025] Furthermore, the step S103 specifically involves substituting the system motion equation into the integral expression of the numerical integration method to solve the dynamic response time history of the bridge and the train.

[0026] Furthermore, the dynamic response of the bridge in step S2 is specifically a displacement response time sequence of each node of the bridge main beam.

[0027] The beneficial effects of the present invention are as follows: the present invention utilizes the bridge stiffness, train parameters and other information contained in the initial stage displacement of the bridge during the vehicle-bridge coupling, and extracts the features in the bridge displacement time series through the LSTM neural network, so as to achieve the purpose of intelligent prediction of subsequent long-term bridge displacement, thereby accelerating the vehicle-bridge coupling calculation and adapting to the complex situation of multiple types and multiple spans of railway bridges. At the same time, as an excellent development of the RNN recurrent neural network, the LSTM neural network maintains its ability to recursively predict time series and overcomes the gradient vanishing or gradient exploding problems that may occur in the RNN. The present invention overcomes the shortcomings of low computational efficiency and long time consumption of the prior art, and is beneficial to the needs of high-frequency or real-time operation data of subsequent intelligent transportation systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 The figure is a flow chart of the method of the present invention.

[0029] Figure 2Schematic diagram of the bridge sample model for the data set calculated using the vehicle-bridge coupling theory.

[0030] Figure 3 Schematic diagram of the LSTM neural network structure.

[0031] Figure 4 This is the result diagram of bridge displacement calculation based on vehicle-bridge theory and LSTM neural network. DETAILED DESCRIPTION

[0032] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0033] like Figure 1 As shown, in one embodiment of the present invention, a vehicle-line-bridge coupled vibration acceleration calculation method based on the LSTM algorithm includes the following steps:

[0034] S1. Based on the vehicle-bridge coupling theory, a vehicle-bridge coupling calculation model is established to solve the dynamic response time history of bridges and trains;

[0035] S2, obtaining several groups of bridge information, using the vehicle-bridge coupling calculation model to obtain the dynamic response of the bridge, and establishing a corresponding relationship data set between the initial response and the subsequent response of the bridge, wherein the subsequent response is the response after the initial response moment;

[0036] S3, using the data set of the correspondence between the initial response and the subsequent response of the bridge response to train the LSTM neural network, and obtain a trained LSTM network;

[0037] S4. Input new bridge information, and use the trained LSTM network to directly recursively derive subsequent bridge responses from the bridge responses calculated by the vehicle-bridge coupling calculation model at the previous time, thereby accelerating the vehicle-bridge coupling calculation.

[0038] The step S1 is specifically as follows:

[0039] S101. Establish a finite element model for the bridge based on the train-bridge coupling theory, and establish a multi-body dynamics model for the train;

[0040] S102, based on the finite element model and the multi-body dynamics model, the track irregularity is used as an excitation to construct the system motion equation;

[0041] S103, solving the system motion equation in the time domain by a numerical integration method to obtain the dynamic response time history of the bridge and the train;

[0042] S104. Construct a vehicle-bridge coupling calculation model based on steps S101-S103.

[0043] The expression of the system motion equation in step S102 is:

[0044]

[0045] F V-B =k wi ×D B

[0046] D Bi =X Bi +r i

[0047] Among them, M V is the mass matrix of the train subsystem; is the acceleration vector of the train subsystem; C V is the damping matrix of the train subsystem; is the speed of the train subsystem; K V is the stiffness matrix of the train subsystem; X V is the displacement of the train subsystem; F V-B and F B-V are the interaction forces between the train and the bridge; M B is the mass matrix of the bridge subsystem; is the acceleration vector of the bridge subsystem; C B is the damping matrix of the bridge subsystem; is the speed of the bridge subsystem; K B is the stiffness matrix of the bridge subsystem; X B is the displacement of the bridge subsystem; k wi is the stiffness of each wheelset of the train; D B The actual position of the bridge space under each wheel; D Bi is the actual position of the i-th node of the bridge; X Bi is the dynamic displacement of the ith node of the bridge subsystem; r i is the unevenness value at the bridge node i.

[0048] The integral expression of the numerical integration method in step S103 is:

[0049]

[0050] Among them, X n+1 is the displacement of the n+1th integration step; Δt is the time integration step; α and β are both integration parameters; is the acceleration vector of the n+1th integration step; is the velocity of the n+1th integration step.

[0051] The step S103 specifically involves substituting the system motion equation into the integral expression of the numerical integration method to solve the dynamic response time history of the bridge and the train.

[0052] In this embodiment, specifically, in the vehicle-bridge coupling theory, a finite element model is used to model the bridge, a multi-rigid body kinematic model is adopted for the train, track unevenness is used as system excitation, the system motion equation is constructed, and it is solved by a numerical integration method.

[0053] Kinematic equations of the train subsystem:

[0054] Kinematic equations of the bridge subsystem:

[0055] Where M V , C V , K V are the mass matrix, damping matrix, and stiffness matrix of the train subsystem respectively; M B , C B , K B are the mass matrix, damping matrix, and stiffness matrix of the bridge subsystem respectively; X V , are the displacement, velocity and acceleration vectors of the train subsystem respectively; X B , are the displacement, velocity and acceleration vectors of the bridge subsystem respectively; F V-B 、F B-V is the interaction force between the train and the bridge.

[0056] The interaction force between the train and the bridge is calculated using the D'Alembert principle and the relative displacement of the vehicle and bridge. The calculation formula is as follows:

[0057] F V-B =k wi ×D B

[0058] In the formula, k wi is the stiffness of each wheelset of the train, D B For each wheel, the actual position of the bridge space under the wheel can be obtained by reading the track irregularity at that position and comparing it with the bridge deformation X at that position. Bi Add them together and the actual position is calculated as follows:

[0059] D Bi =X Bi +r i

[0060] Where D Biis the actual position of the i-th node of the bridge, X Bi are the dynamic displacement of the i-th node of the bridge subsystem, r i is the unevenness value at the corresponding bridge node i;

[0061] Specifically, the numerical integration method for solving the system motion equation is the Newmark-β method. The displacement, velocity and acceleration of the bridge subsystem are calculated by the Newmark-β method; the integration format is:

[0062]

[0063] Where α and β are integration parameters, which can generally be taken as 0.25 and 0.5 respectively; Δt is the time integration step; n represents the nth integration step;

[0064] The displacement of the bridge subsystem X B ,speed Acceleration vector As X n , Substituting this into the equation, we can solve the equation of motion of the bridge subsystem;

[0065] In the above formula Utilizing X n+1 To represent, then respectively Substitute into the bridge subsystem dynamics equation at time n+1 and simplify to obtain X n+1 The solution formula is:

[0066]

[0067] In the formula, F n+1 is the bridge node load at time n+1; M, C, and K are the mass matrix, damping matrix, and stiffness matrix, respectively.

[0068] X n+1 The solution formula is:

[0069]

[0070] In the formula, the intermediate quantity Intermediate Intermediate Intermediate Intermediate Intermediate Intermediate quantity a6 = Δt(1-β), intermediate quantity a7 = βΔt, solving the above equation yields X n+1 ;

[0071] The solution formula is as follows:

[0072]

[0073] The dynamic response of the bridge in step S2 is specifically a displacement response time sequence of each node of the bridge main beam.

[0074] In this embodiment, the train model is CRH3, and the speed is uniformly set to 200km / h. Figure 2 As shown in the figure, there are 50 railway bridges, including a main span of 1092m suspension bridge, a 32m simply supported beam bridge, and a 40m simply supported beam bridge. Their finite element models are established respectively, and the vehicle-bridge coupling analysis theory is used to solve their vehicle-driven force response, mainly including the displacement time history curves of each node of the bridge. Figure 2 As shown in the figure, the mid-span node displacement time history of the vehicle-induced force response of the main span 1092m suspension bridge is given. The train is divided according to the time it takes to cross the bridge, and the time database corresponding to the front and back time is established.

[0075] Establish a neural network based on the LSTM model and initialize it:

[0076] Specifically, the main structure of the LSTM neural network (Long short term memory network) is the memory unit, including the forget gate, memory gate and output gate. The specific functions of each part are as follows: the forget gate selectively forgets the information of the previous node; the memory gate selects the effective information and selectively passes it to the next unit according to the importance of the information; the output gate determines the output information.

[0077] like Figure 3 The following is the structure diagram of the LSTM neural network. “×” indicates the scaling of information, “+” indicates the addition of information, σ is the Sigmoid function, tanh is the hyperbolic tangent function, and h t-1 is the output of the previous memory unit, x t is the input information of this layer, h t is the output of the memory unit. Specifically, through the forget gate, memory gate and output gate, the LSTM neural network can screen the transmitted information and filter out unimportant information to achieve the purpose of managing information transmission.

[0078] In this embodiment, the model is initialized using a transfer learning method. Compared with directly assigning random values ​​to neural network parameters, transfer learning can transfer some neural network structural features or annotated data from related fields, thereby speeding up training and improving accuracy.

[0079] Divide the data set into training set and test set according to the proportion. Train the neural network to obtain the optimal model, and test and verify it:

[0080] Specifically, in this embodiment, the data set is divided into a ratio of 6:4. The learning rate and the total number of iterations are mainly controlled. By comparing the relationship curve between the loss function and the number of iterations, the learning rate is preferentially determined. When the loss function gradually converges with the increase in the number of iterations, the optimal model can be determined. Then the effect is verified through the test set. Figure 4 The bridge displacement time history curve is given, and the vehicle-bridge coupling calculation results and LSTM network prediction results are given. The mean square error is calculated by the predicted value and the calculated value, and the formula is as follows:

[0081]

[0082] Specifically, N is the total number of samples, and i' is the sample number. In this embodiment, the mean square error is less than 0.1, and it is considered that the accuracy of the model after training meets the requirements.

[0083] Input new bridge information, and directly recursively calculate the subsequent bridge response from the bridge response calculated by vehicle-bridge coupling at the previous time through the LSTM network, replacing the numerical integration solution process of the original dynamic equation;

[0084] In this embodiment, a railway suspension bridge with a main span of 1092 m is selected to perform traditional vehicle-bridge coupling calculation and vehicle-bridge coupling calculation based on LSTM acceleration.

[0085] Specifically, the bridge deformation X B In the vehicle-bridge coupling theory calculation, the bridge motion equation is solved by the Newmark-β method, and the bridge deformation X B It contains information about the bridge's own stiffness, mass, damping, etc., as well as the train's response information after acting on the bridge as a moving load, and is a key variable in vehicle-bridge coupling. Through the LSTM neural network, the response time series in the subsequent time period is recursively derived from the bridge response information in the previous time period to achieve the purpose of acceleration. Table 1 shows the comparison between the theoretical calculation time of vehicle-bridge coupling for the three bridges and the calculation time after acceleration using machine learning. It can be seen that the solution speed is significantly improved by recursively replacing the numerical integration method with the neural network.

[0086] Table 1 Comparison of axle coupling calculation time after acceleration

[0087]

[0088] This method is based on the traditional vehicle-bridge coupling calculation theory. By introducing the LSTM neural network for predicting the bridge response displacement time history, the dynamic response of the bridge at the front moment can be calculated through vehicle-bridge coupling, and the complete bridge displacement response of the train crossing the bridge can be recursively obtained. Subsequent vehicle responses can be quickly calculated based on the bridge displacement. It overcomes the shortcomings of low calculation efficiency and long time consumption of the existing technology, and is conducive to the needs of high-frequency or real-time operation data of subsequent intelligent transportation systems.

Claims

1. A vehicle-line-bridge coupled vibration acceleration calculation method based on LSTM algorithm, characterized in that: The following steps are involved: S1. Based on the vehicle-bridge coupling theory, a vehicle-bridge coupling calculation model is established to solve the dynamic response time history of bridges and trains; S2, obtaining several groups of bridge information, using the vehicle-bridge coupling calculation model to obtain the dynamic response of the bridge, and establishing a corresponding relationship data set between the initial response and the subsequent response of the bridge, wherein the subsequent response is the response after the initial response moment; S3, using the data set of the correspondence between the initial response and the subsequent response of the bridge response to train the LSTM neural network, and obtain a trained LSTM network; S4. Input new bridge information, and use the trained LSTM network to directly recursively derive subsequent bridge responses from the bridge responses calculated by the vehicle-bridge coupling calculation model at the previous time, thereby accelerating the vehicle-bridge coupling calculation.

2. The vehicle-line-bridge coupled vibration acceleration calculation method based on the LSTM algorithm according to claim 1 is characterized in that: The step S1 is specifically as follows: S101. Establish a finite element model for the bridge based on the train-bridge coupling theory, and establish a multi-body dynamics model for the train; S102, based on the finite element model and the multi-body dynamics model, the track irregularity is used as an excitation to construct the system motion equation; S103, solving the system motion equation in the time domain by a numerical integration method to obtain the dynamic response time history of the bridge and the train; S104. Construct a vehicle-bridge coupling calculation model based on steps S101-S103.

3. The vehicle-line-bridge coupled vibration acceleration calculation method based on the LSTM algorithm according to claim 2 is characterized in that: The expression of the system motion equation in step S102 is: F V-B =k wi ×D B D Bi =X Bi +r i Among them, M V is the mass matrix of the train subsystem; is the acceleration vector of the train subsystem; C V is the damping matrix of the train subsystem; is the speed of the train subsystem; K V is the stiffness matrix of the train subsystem; X V is the displacement of the train subsystem; F V-B and F B-V are the interaction forces between the train and the bridge; M B is the mass matrix of the bridge subsystem; is the acceleration vector of the bridge subsystem; C B is the damping matrix of the bridge subsystem; is the speed of the bridge subsystem; K B is the stiffness matrix of the bridge subsystem; X B is the displacement of the bridge subsystem; k wi is the stiffness of each wheelset of the train; D B The actual position of the bridge space under each wheel; D Bi is the actual position of the i-th node of the bridge; X Bi is the dynamic displacement of the ith node of the bridge subsystem; r i is the unevenness value at the bridge node i.

4. The vehicle-line-bridge coupled vibration acceleration calculation method based on the LSTM algorithm according to claim 2 is characterized in that: The integral expression of the numerical integration method in step S103 is: Among them, X n+1 is the displacement of the n+1th integration step; Δt is the time integration step; α and β are both integration parameters; is the acceleration vector of the n+1th integration step; is the velocity of the n+1th integration step.

5. The vehicle-line-bridge coupled vibration acceleration calculation method based on the LSTM algorithm according to claim 2 is characterized in that: The step S103 specifically involves substituting the system motion equation into the integral expression of the numerical integration method to solve the dynamic response time history of the bridge and the train.

6. The vehicle-line-bridge coupled vibration acceleration calculation method based on the LSTM algorithm according to claim 1 is characterized in that: The dynamic response of the bridge in step S2 is specifically a displacement response time sequence of each node of the bridge main beam.

Images