Vehicle-Line-Bridge Coupled Vibration Acceleration Calculation Method Based on LSTM Algorithm

Abstract

The present invention discloses a vehicle-line-bridge coupled vibration acceleration calculation method based on the LSTM algorithm, belonging to the field of vehicle-bridge coupling calculation acceleration. The method includes establishing a vehicle-bridge coupling calculation model for solving the time history of the dynamic responses of the bridge and the train based on the vehicle-bridge coupling theory; obtaining several groups of bridge information, using the vehicle-bridge coupling calculation model to obtain the dynamic response of the bridge, and establishing a data set of the corresponding relationship between the initial response and the subsequent response of the bridge response; training the LSTM neural network using the data set of the corresponding relationship between the initial response and the subsequent response of the bridge response to obtain a trained LSTM network; inputting new bridge information, and directly recursively obtaining the subsequent bridge response from the bridge response calculated by the vehicle-bridge coupling calculation model at the previous time using the trained LSTM network, so as to complete the acceleration of the vehicle-bridge coupling calculation. The present invention solves the problems of time-consuming calculation and low efficiency in the existing vehicle-bridge coupling calculation.

Description

Technical Field

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

[0002] With the development of high-speed railway bridges in China towards more complex and flexible structures, and at the same time, the speed of railway trains is constantly increasing. When a train crosses a bridge, it will first cause the deformation and vibration of the bridge, directly affecting 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 crossing the bridge, and even in extreme cases, it will lead to serious accidents such as train derailment. Therefore, the research on the coupled dynamic calculation of trains and bridges is of great significance for improving the structural stability and durability of bridges as well as 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 face challenges in quickly adapting to the changing conditions of bridges under different loads and environmental impacts, resulting in low computational efficiency.

[0004] An existing technical solution is based on the structural dynamics theory of multi-system coupling, and calculates the dynamic response of the bridge and vehicle when a train crosses a combined road-rail bridge. This method has clear theory and clear results. However, this method involves solving the numerical integration method of large-scale structural dynamics matrices, which requires high computer performance and is relatively time-consuming. Summary of the Invention

[0005] Aiming at the above deficiencies in the prior art, a vehicle-line-bridge coupling vibration acceleration calculation method based on the LSTM algorithm provided by the present invention solves the problems of time-consuming calculation and low efficiency in existing vehicle-bridge coupling calculations.

[0006] To achieve the above invention purpose, the technical solution adopted by the present invention is: a vehicle-line-bridge coupling vibration acceleration calculation method based on the LSTM algorithm, including the following steps:

[0007] S1. Based on the vehicle-bridge coupling theory, establish a vehicle-bridge coupling calculation model for solving the time history of the dynamic response of the bridge and the train;

[0008] S2. Obtain several groups of bridge information, use the vehicle-bridge coupling calculation model to obtain the dynamic response of the bridge, and establish a data set of the corresponding relationship between the initial response and the subsequent response of the bridge, where the subsequent response is the response after the initial response time;

[0009] S3. Use the dataset of the corresponding relationship between the initial response and subsequent responses of the bridge to train the LSTM neural network, and obtain the trained LSTM network.

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

[0011] Further, the specific steps of step S1 are as follows:

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

[0013] S102. According to the finite element model and the multi-body dynamics model, take the track irregularity as the excitation and construct the system motion equation.

[0014] S103. Solve the system motion equation in the time domain by numerical integration method to obtain the time history of the dynamic responses of the bridge and the train.

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

[0016] Further, 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] where, 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 velocity 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 velocity 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 wheel pair of the train; D B is 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 i-th node of the bridge subsystem; r i is the unevenness value at the position of bridge node i.

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

[0023]

[0024] where X n+1 is the displacement at the (n + 1)-th integration step; Δt is the time integration step size; α and β are both integration parameters; is the acceleration vector at the (n + 1)-th integration step; is the velocity at the (n + 1)-th integration step.

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

[0026] Further, the dynamic response of the bridge in step S2 is specifically the displacement response time series of each node of the bridge main girder.

[0027] The beneficial effects of the present invention are as follows: By using the information such as the bridge stiffness and train parameters contained in the displacement at the initial stage of the bridge in the vehicle-bridge coupling effect, the present invention extracts the features in the bridge displacement time series through the LSTM neural network, so as to achieve the purpose of intelligent prediction of the subsequent long-term bridge displacement, thereby accelerating the vehicle-bridge coupling calculation and adapting to the complex situations 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 problems of gradient disappearance or gradient explosion that may occur in the RNN. The present invention overcomes the disadvantages of low calculation efficiency and long time consumption in the prior art, and is conducive to the requirements of high-frequency or real-time operation data of the subsequent intelligent transportation system. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 is the flowchart of the method of the present invention.

[0029] Figure 2Schematic diagram of a bridge sample model for a dataset calculated using vehicle-bridge coupling theory.

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

[0031] Figure 4 Result graph of bridge displacement calculation based on vehicle-bridge theory and LSTM neural network. Specific implementation manners

[0032] The following describes the specific implementation manners of the present invention to facilitate those skilled in the art of the present technology to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation manners. For those of ordinary skill in the art of the present technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions created using the concept of the present invention are within the scope of protection.

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

[0034] S1. Based on the vehicle-bridge coupling theory, establish a vehicle-bridge coupling calculation model for solving the time history of the dynamic responses of the bridge and the train.

[0035] S2. Obtain several groups of bridge information, use the vehicle-bridge coupling calculation model to obtain the dynamic response of the bridge, and establish a dataset of the corresponding relationship between the initial response and the subsequent response of the bridge response, where the subsequent response is the response after the initial response moment.

[0036] S3. Use the dataset of the corresponding relationship between the initial response and the subsequent response of the bridge response to train the LSTM neural network to obtain a trained LSTM network.

[0037] S4. Input new bridge information, and use the trained LSTM network to directly recursively obtain the subsequent bridge response from the bridge response calculated by the vehicle-bridge coupling calculation model at the previous time to complete the acceleration of the vehicle-bridge coupling calculation.

[0038] The specific content of step S1 is as follows:

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

[0040] S102. According to the finite element model and the multi-body dynamics model, use the track irregularity as the excitation to construct the system motion equation.

[0041] S103. Solve the system motion equation in the time domain by numerical integration method to obtain the time history of the dynamic responses of the bridge and the train.

[0042] S104. Build 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] where, 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 velocity 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 velocity 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 wheel pair of the train; D B is 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 i-th node of the bridge subsystem; r i is the unevenness value at the position of bridge node i.

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

[0049]

[0050] where, X n+1 is the displacement at the (n + 1)-th integration step; Δt is the time integration step size; α and β are both integration parameters; is the acceleration vector at the (n + 1)-th integration step; is the velocity at the (n + 1)-th integration step.

[0051] Specifically, in step S103, the dynamic response time history of the bridge and the train is solved by substituting the system motion equation into the integration expression of the numerical integration method.

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

[0053] Kinematic equation of the train subsystem:

[0054] Kinematic equation of the bridge subsystem:

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

[0056] The interaction force between the train and the bridge is obtained by using D'Alembert's principle and based on the relative displacement between the vehicle and the 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 wheel pair of the train, D B is the actual position of the bridge space under each wheel, which can be obtained by reading the track irregularity at this position and adding it to the bridge deformation X Bi at this position. The calculation formula for the actual position is as follows:

[0059] D Bi = X Bi + r i

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

[0061] Specifically, the numerical integration method for solving the system motion equation is the Newmark-β method. The displacements, velocities and accelerations 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 n-th integration step;

[0064] The displacement X B and velocity acceleration vector of the bridge subsystem are respectively used as X n , substituted into it, and the motion equation of the bridge subsystem can be solved;

[0065] In the above formula, is expressed by using X n+1 , and then are respectively substituted into the dynamic equation of the bridge subsystem at the (n + 1)-th moment, and after simplification, the solution formula of X n+1 is obtained:

[0066]

[0067] where F n+1 is the bridge node load at the (n + 1)-th moment; M, C, and K are the mass matrix, damping matrix, and stiffness matrix

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

[0069]

[0070] where the intermediate quantity intermediate quantity intermediate quantity intermediate quantity intermediate quantity intermediate quantity The intermediate quantity a6 = Δt(1 - β), the intermediate quantity a7 = βΔt, and solving the above formula gives X n+1 ;

[0071] The solution formula of

[0072]

[0073] In step S2, the dynamic response of the bridge specifically refers to the displacement response time series of each node of the bridge girder.

[0074] In this embodiment, the train model is selected as CRH3 and the vehicle speed is uniformly 200 km / h. Some bridge models are as Figure 2 shown, including 50 railway bridges such as a suspension bridge with a main span of 1092 m, a 32 m simply supported beam bridge, and a 40 m simply supported beam bridge. Their finite element models are established respectively, and the vehicle-induced dynamic response is solved using the vehicle-bridge coupling analysis theory, mainly including the displacement time history curves of each node of the bridge. As Figure 2 shown, the mid-span node displacement time history of the vehicle-induced dynamic response of the suspension bridge with a main span of 1092 m is given. It is divided according to the train crossing time, divided by 1 / 10 of the total duration, and a database of corresponding front and back times is established.

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

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

[0077] As Figure 3 shown, it is the structure diagram of the LSTM neural network. "×" represents the scaling of information, "+" represents the addition of information, σ is the Sigmoid function, tanh is the hyperbolic tangent function, h t-1 is the output of the previous memory unit, x t is the input information of this layer, and h t is the output of this memory unit. Specifically, through the forget gate, the input gate, and the 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 initialization of the model adopts the transfer learning method. Compared with directly randomly assigning values to the neural network parameters, transfer learning can transfer some neural network structure features or labeled data from related fields, thereby accelerating the training speed and improving the accuracy.

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

[0080] Specifically, in this embodiment, the division ratio of the data set is 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 determined first. When the loss function gradually converges with the increase of the number of iterations, the optimal model can be determined. Then, the effect is verified through the test set. Figure 4 The time history curve of the bridge displacement is given, and the calculation results of the vehicle-bridge coupling and the prediction results of the LSTM network 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; i' is the sample number. In this embodiment, the mean square error is less than 0.1, and it is considered that the accuracy after model training meets the requirements.

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

[0084] In this embodiment, a railway suspension bridge with a main span of 1092m is selected, and the traditional vehicle-bridge coupling calculation and the vehicle-bridge coupling calculation accelerated by LSTM are carried out respectively.

[0085] Specifically, the bridge deformation X B In the theoretical calculation of vehicle-bridge coupling, it is obtained by solving the bridge motion equation through the Newmark-β method. The bridge deformation X B Contains information such as the stiffness, mass, and damping of the bridge itself, and also contains the response information of the bridge after the action of the train as a moving load. It is a key variable in vehicle-bridge coupling. Through the LSTM neural network, the response time series in the subsequent time is recursively calculated from the bridge response information in the previous time to achieve the acceleration purpose. Table 1 shows the comparison of the theoretical calculation time of vehicle-bridge coupling for three bridges and the calculation time after acceleration by machine learning. It can be seen that the speed of solving by replacing the numerical integration method with neural network recursion is significantly improved.

[0086] Table 1 Comparison of the calculation time of vehicle-bridge coupling after acceleration

[0087]

[0088] This method is based on the traditional vehicle-bridge coupling calculation theory. By introducing the LSTM neural network for the prediction of the time history of the bridge response displacement, only the dynamic response of the bridge in the previous section of time needs to be calculated by the vehicle-bridge coupling, and the complete bridge displacement response of the train crossing the bridge can be recursively calculated. The subsequent vehicle response, etc., can be quickly calculated based on the bridge displacement. It overcomes the disadvantages of low calculation efficiency and long time consumption in the existing technology, and is beneficial to the needs of high-frequency or real-time operation data of the subsequent intelligent transportation system.

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 data set of corresponding relationships between the initial response and the subsequent response of the bridge, wherein the subsequent response is the response after the initial response moment; the dynamic response of the bridge in step S2 is specifically a displacement response time sequence of each node of the bridge main beam; 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.

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