CN117669389B - Random vibration analysis method for earthquake-vehicle-bridge system based on deep learning - Google Patents

Random vibration analysis method for earthquake-vehicle-bridge system based on deep learning Download PDF

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CN117669389B
CN117669389B CN202410131537.5A CN202410131537A CN117669389B CN 117669389 B CN117669389 B CN 117669389B CN 202410131537 A CN202410131537 A CN 202410131537A CN 117669389 B CN117669389 B CN 117669389B
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朱思宇
杨梦雪
向天宇
徐昕宇
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Xihua University
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Abstract

The invention relates to the technical field of seismic design of bridges, and discloses a seismic-vehicle-bridge system random vibration analysis method based on deep learning, wherein a proposed model comprises three modules: the system comprises a CNN module for seismic data feature extraction, an attention mechanism module for enhancing information selection among time sequences and improving the accuracy and efficiency of final prediction, and a bi-directional gating recursion unit (BiGRU) for predicting axle system response, wherein the model establishes mapping connection between seismic excitation and train response; the proposed model was validated using trains operating under near fault earthquake and real railway cable stayed bridges. Uncertainty of train weight and bridge damping ratio is also considered; finally, a CNN-BiGRU model based on an attention mechanism is customized and established based on the training data. The time-varying response of the proposed model is highly consistent with the results of the validated dynamic axle system.

Description

Random vibration analysis method for earthquake-vehicle-bridge system based on deep learning
Technical Field
The invention relates to the technical field of seismic design of bridges, in particular to a random vibration analysis method of an earthquake-vehicle-bridge system based on deep learning.
Background
In the past few decades, the High Speed Railway Network (HSRN) of china has evolved rapidly. High-speed railways have become the first choice for travel and business trips due to their remarkable efficiency, convenience and punctuality. By 2022, the China's high-speed railway network has been extended to over 42,000 km, which connects various areas and promotes the development of regional economy. Thus, high-speed railway networks must face unavoidable seismic risks during construction and operation, particularly considering that china is located in the eurasia and the pacific seismic bands. At the same time, as high speed vehicles tend to be faster and lighter, bridges are widely used in high speed railway networks to ensure the smoothness of the track. When an earthquake occurs, the probability of the vehicle passing the bridge increases significantly. In the past two decades, several high-speed railway vehicle accidents caused by earthquakes have occurred, and thus it has become critical to ensure the safety of the travel of vehicles on bridges under seismic excitation.
In particular, near-fault earthquakes present an unavoidable and arduous challenge to the seismic design of bridges in high-speed railway networks, given that large-span bridges of railways are often located at or pass through unstable junctions of structural slabs. Near-fault earthquakes have larger velocity pulses and longer pulse periods than far-field earthquakes. Researchers have achieved some success regarding the dynamic response characteristics of near-fault seismic induced structures. The structural response caused by near-fault seismic excitation is significantly different from that caused by general seismic excitation, so that special attention is required to the multi-degree-of-freedom structure under the near-fault seismic action. Near-fault seismic has a substantial impact on the dynamic response of the bridge due to low frequency resonance. In order to ensure smooth operation of the high-speed railway system, the concept of "replacing a railway line with a bridge" has been implemented, and thus the dynamic response of the vehicle-bridge system has become one of the most focused research subjects in the civil engineering field. With the destructive disclosure of near-fault earthquake, the driving safety of trains on bridges under the action of near-fault earthquake becomes another important view angle. In general, in the research of the vehicle safety of an axle system under the earthquake condition, the research of the vehicle safety of the axle system under the action of a near-fault earthquake is relatively limited. At the same time, the unavoidable randomness of the earthquake and the uncertainty of the parameters of the axle system should be also included in the dynamic analysis of the axle system under the action of the near-fault earthquake.
Currently, many studies focus on random vibrations of train-bridge systems under seismic action. In these studies, a key issue is to handle random excitation or uncertainty parameters to reduce the sampling required for dynamic response, thereby increasing computational efficiency. However, hundreds of simulations are required to ensure computational accuracy. Therefore, as an alternative to axle models, simplified proxy models with lower computational overhead than the coarse Monte Carlo Method (MCM) are of increasing interest. Among the various types of simplified proxy models, the deep learning model is a current popular choice at its lower computational cost.
At present, a plurality of researches fully prove that the deep learning has good performance and application prospect on an axle system. However, deep learning model studies for the operational safety assessment of axle systems under near-fault seismic action are relatively limited. Thus, the key challenges of uncertain system operation safety analysis in near-fault earthquakes include three components: (1) complex significant stochastic properties should be incorporated into the calculation; (2) The calculation cost can be further reduced by an artificial intelligence method; (3) The application of the deep learning method in the random analysis of the axle system has not been confirmed.
Disclosure of Invention
Aiming at the problems, the invention aims to provide a deep learning-based seismic-vehicle-bridge system random vibration analysis method, which utilizes the strong feature extraction capability of convolution to capture the features of random seismic data, dynamically and adaptively focuses on the effective parts of the features through a focusing mechanism, ignores irrelevant parts and finally realizes the whole process one-step prediction of the response of a vehicle-bridge coupling random vibration system through BiGRU; the mapping between the random seismic waves and the axle coupling random vibration system is established, the purposes of improving the calculation efficiency and reducing the calculation cost are achieved, and meanwhile, the response of the uncertainty axle system can be accurately predicted. The technical proposal is as follows:
the random vibration analysis method of the earthquake-vehicle-bridge system based on deep learning comprises the following steps:
step 1: establishing a train model and a bridge model, extracting self-vibration frequency and vibration mode data of the train model and the bridge model, and verifying the correctness of the bridge model through data obtained by analysis and calculation;
step 2: according to the design technical specification of a real large-span cable-stayed railway bridge, determining a seismic peak acceleration value, a seismic response spectrum characteristic period and a bridge design speed per hour at a bridge position;
step 3: acquiring seismic wave data according to a seismic design response spectrum, and performing amplitude processing on the seismic wave data according to a seismic vibration peak acceleration value at a bridge position;
step 4: determining a variation coefficient Cov of the self-weight of the train and the damping ratio of the bridge, and obtaining random parameters of the self-weight of the train and the damping ratio of the bridge through Monte Carlo sampling according to the variation coefficient and the average value;
step 5: according to the processed seismic wave data, the self-vibration frequency and vibration mode data of the axle model, and the fixed parameters and the random parameters of the determined dead weight of the train and the damping ratio of the bridge, calculating to obtain the response of the corresponding axle coupling system, and evaluating the operation safety and stability;
step 6: setting fixed parameters of the set number of seismic wave data and the determined dead weight of the train and the bridge damping ratio as input data, and forming a data set 1 with the corresponding axle coupling system response calculated in the step 5; setting the set number of seismic wave data and random parameters of the dead weight of the train and the damping ratio of the bridge obtained in the step 4 as input data, and forming a data set 2 with the response of the corresponding axle coupling system calculated in the step 5;
step 7: constructing a CNN-Attention-BiGRU deep learning combination network, verifying the prediction correctness of the CNN-Attention-BiGRU deep learning combination network, and performing super-parameter setting on the CNN-Attention-BiGRU deep learning combination network before training by combining actual data;
step 8: inputting the data set 1 into a CNN-Attention-BiGRU deep learning combination network for prediction training to obtain a prediction model of deterministic train dead weight and bridge damping ratio parameters, and verifying the prediction accuracy of the network under deterministic parameter conditions;
step 9: inputting the data set 2 into a CNN-Attention-BiGRU deep learning combination network for prediction training to obtain a prediction model of the self weight of the uncertain train and the damping ratio parameters of the bridge, and verifying the prediction accuracy of the network under the condition of the uncertain parameters;
step 10: and obtaining more response samples of the axle coupling random vibration system through the CNN-Attention-BiGRU deep learning combination network, and calculating the mean value and standard deviation according to the response samples.
Further, the CNN-Attention-BiGRU deep learning combination network comprises three modules: an encoder module, an attention mechanism module, and a decoder module; the method comprises the following steps:
the encoder module is used for extracting the characteristics of the seismic data time sequence and comprises a one-dimensional convolution layer, a LeakyReLU nonlinear mapping layer and a Dropout layer; mapping the one-dimensional time sequence to a high-dimensional space by the one-dimensional convolution layer to obtain multi-dimensional characteristics; the Dropout layer is used for preventing overfitting;
the attention mechanism module is used for weighting the multidimensional features, focusing on the key features and reducing the attention to other information so as to improve the efficiency and accuracy of task processing;
the decoder module is used for predicting the response of the axle coupling system and comprises a BiGRU layer and a full-connection layer;
the algorithm employs a direct one-step generation of the complete sequence.
Further, the specific calculation in the CNN-Attention-BiGRU deep learning combination network is as follows:
the one-dimensional convolution layer in the encoder module extracts features in a one-dimensional time sequence, and the calculation of convolution is expressed as a matrix form:
（1）；
wherein,N cov andMconvolution output and input, respectively;Cis a sparse matrix of convolution kernels,representing a convolution operator;bis a bias term;
the attention mechanism module further weights the characteristics output by the encoder module, dynamically and adaptively focuses on different parts of the characteristics, and provides better prediction precision for the prediction of the target sequence; the attention mechanism module calculates the similarity between each element in the target output and input sequence, and obtains the weight of each element; then using these weights to calculate a weighted sum of the input sequence elements to obtain a weighted sum vector, which is taken as the output of the attention mechanism module; the calculation is as follows:
（2）；
wherein,ais the output of the attention mechanism module;his the output of the encoder and the input of the attention mechanism;W v 、W k andW q is a weight matrix of the attention module;K＝hW k is the key vector of the key vector,Q＝hW q is a query vector;V=hW v as a vector of values,as a function of the score,dthe length of the query vector and the key vector;Ttranspose the symbol;
the BiGRU in the CNN-Attention-BiGRU algorithm is used for predicting and outputting data; the biglu comprises a front and back 2 GRU units, which include two key components: an update gate to determine how much past state should be preserved and considered, and how to combine new input information with previous state information to help the GRU maintain long term memory; reset gate is used to determine how much previous information should be forgotten and can be effectivelyDiscarding irrelevant data; update doorz t Reset gater t The following is shown:
（3）；
（4）；
wherein,W z andU z respectively representing the weight matrix learned by the update gate during training and the weight matrix determined at the end of training,W r andU r respectively representing a weight matrix learned by the reset gate during training and a weight matrix determined at the end of training;is a sigmoid function;x t is an input of the current time step,h t-1 is thatt-hidden state of 1 time step;b z in order to update the bias of the gate,b r bias for reset gate; the reset gate calculates the hidden state, and the update gate updates the hidden state; the detailed calculation is as follows:
（5）；
（6）；
wherein,is a hyperbolic tangent function, ">Is the Hadamard product, ">An update candidate state representing time t;W h andU h as a matrix of weights that can be learned,b h in order for the offset to be a function of,h t is thattA hidden state of the time step;
when (when)z t When the state is converged to 1, the candidate hidden state which is calculated newly is ignored, and the past state is not updated; when (when)z t When converging to 0, the candidate hidden state is preserved; when the sequence has short-term dependency, the reset gate is in an active state; when the sequence has long-term dependence, the update gate is in an active state;
BiGRU obtains two-way timing dependencies by concatenating 2 GRUs in opposite directions, and the parameterized formula for BiGRU is as follows:
（7）；
（8）；
（9）；
wherein,is a hidden state of forward propagation, +.>Is a hidden state of back propagation and is,α t andβ t the weights of the forward propagating hidden state and the backward propagating hidden state respectively,b t is a bias vector.
Compared with the prior art, the invention has the beneficial effects that:
the invention mainly takes random earthquake and the dead weight of an uncertainty train as input data and takes an uncertainty axle system response sample as output data to construct a training data set, and the data set is input into a CNN-Attention-BiGRU deep learning combination network for training and prediction. The method utilizes the strong characteristic extraction capability of convolution to capture the characteristics of the random seismic data, dynamically and adaptively focuses on the effective parts of the characteristics through a focusing mechanism, ignores irrelevant parts, and finally realizes the whole-process one-step prediction of the response of the axle coupling random vibration system through the BiGRU (bi-directional gating recursion unit). The deep learning algorithm establishes mapping between the random seismic waves and the axle coupling random vibration system, achieves the purposes of improving the calculation efficiency and reducing the calculation cost, and can accurately predict the response of the uncertainty axle system; the sample prediction error obtained by the method is within the engineering allowable range, the effect can reach the actual requirement, an effective solving way is provided for solving the problems of difficult modeling, complex calculation process, time consumption and the like in the traditional engineering, and the application of artificial intelligence in the traditional engineering is promoted.
Drawings
FIG. 1 is a diagram of a train-bridge system dynamics analysis process.
Fig. 2 is a schematic diagram of an attention module.
Fig. 3 is an illustration of a GRU unit.
FIG. 4 is a diagram of a BiGRU neural network structural element.
Fig. 5 is a schematic diagram of a CAB neural network.
Fig. 6 is a bridge construction layout.
Fig. 7 (a) is a graph showing loss in prediction of train derailment coefficient on bridge under training and learning near fault earthquake action: CAB model.
Fig. 7 (b) is a graph showing loss in prediction of train derailment coefficient on bridge under training and learning near fault earthquake action: BAB model.
Fig. 8 shows derailment coefficients for a single seismic stimulus for parameter determination in example 1.
Fig. 9 shows the prediction of the derailment coefficient of the train when the parameter is not determined in example 1.
Fig. 10 (a) is a graph showing loss in prediction of derailment coefficient for training learning parameter uncertainty: CAB model.
Fig. 10 (b) is a graph showing loss in prediction of derailment coefficient for training learning parameter uncertainty: BAB model.
In example 2 of fig. 11, the derailment coefficient of the train under one seismic excitation is shown.
Detailed Description
The invention will now be described in further detail with reference to the drawings and to specific examples. The invention provides a CNN-Attention-BiGRU (CAB) neural network which is specially designed for analyzing the operation safety of trains on a bridge under the action of near-fault earthquake. The neural network includes three modules, an encoder module, an attention mechanism module, and a decoder module. Wherein the encoder module employs a convolutional layer (CNN) for feature extraction of the seismic data time series. An Attention mechanism module (Attention) is used to enhance information selection between time series to improve accuracy and efficiency of final predictions. The decoder module employs a bi-directional gating recursion unit (BiGRU) for prediction of the output data (operational safety assessment, smoothness assessment). Based on the proposed method, the application and efficiency of the real large-span cable-stayed railway bridge are researched by applying the real large-span cable-stayed railway bridge, and the randomness of the near-fault earthquake and the uncertain train weight and bridge damping ratio are involved in calculation. The method is based on Python language, adopts the Pytorch library to write programs, improves the calculation efficiency by approximately 16 times, reduces the calculation cost by 8 times, and has a certain accuracy level. The technical proposal is as follows:
the random vibration analysis method of the earthquake-vehicle-bridge system based on deep learning comprises the following steps:
step 1: and establishing a train model and a bridge model, extracting self-vibration frequency and vibration mode data of the train model and the bridge model, and verifying the correctness of the bridge model through data obtained by analysis and calculation.
(1) Dynamic model of railway vehicle
The present embodiment assumes that all components of a single consist railway vehicle are rigid and connected by springs and dampers. The vehicle model is considered as a mass-spring-damping dynamic model. The flexibility of the vehicle model is provided by the spring elements, and the dampers act as energy dissipating devices such as rubber pads, shock absorbers and absorbers.
The train was simulated according to a typical chinese CRH2 train. The equation of motion of the train can be expressed as equation (1):
（1）；
wherein,M v 、C v andK v representing the mass, damping and stiffness matrices of the train respectively,、/>andurespectively representing the acceleration, speed and displacement vectors of the train,y b and->Is the velocity and displacement vector of the contact point. Organizing equation (1) to obtain equation (2):
（2）；
the equation is the dynamics equation of the train, and the right side of the equation is the force transmitted by the bridge to the trainF bv ：
（3）；
The forces transmitted by the bridge to the train are caused by vibrations of the bridge. Specifically, the displacement response and velocity response of the bridge are translated into a bridge to train force through the damper and springs of the train.
(2) Finite element model of bridge
Analytical finite element models for continuous rigid frame bridges employ two-node, three-dimensional beam elements having 12 degrees of freedom (DOFs), each element comprising six translational and six rotational degrees of freedom.
The equation of motion of a bridge can be expressed as:
（4）；
wherein,M b 、C b andK b representing the mass, damping and stiffness matrices of the bridge respectively,、/>andwrespectively representing acceleration, speed and displacement vectors of the bridge;f e is the external force vector, referred to herein as seismic excitation.
In addition, the forces transmitted to the bridge by the train through the contact points include the weight, inertial force and damping force of the train:
（5）；
wherein,ggravitational acceleration;F vb andF bv is a pair of force and reaction force.
(3) Dynamic analysis process of vehicle-bridge system
The vehicle-bridge model consists of a vehicle (train) subsystem and a bridge subsystem. These two subsystems need to satisfy a coupling relationship of two aspects:
1) In order to meet the displacement coordination requirement, the wheels and the bridge must be kept in close contact without relative movement;
2) The interaction force of the wheel and the bridge contact point is required to conform to newton's third law.
In particular, forces between the train subsystem and the bridge subsystem are transferred through the contact points. The above equation shows that the coupling system of train-bridge power interactions is time-varying. Thus, it is beneficial to use a separate iterative approach. In each iteration, the difference between the two subsystem responses is calculated until an error limit is met. The vehicle-bridge system dynamics analysis process is shown in fig. 1.
Wheel rail forceF wr （t) Comprising two parts: normal friction forceF Nwr （t) And tangential friction forceF Twr （t). Normal friction force of wheel railF Nwr （t) Is calculated according to the Hertz nonlinear contact theory. Tangential friction forceF Twr （t) Then the Shen-heat formula is used for calculation. The trace method is used to determine the point of contact between the wheel and the track. Wheel rail forceF wr （t) Expressed as a function of the speed and displacement of the wheel set and track. The normal friction of the wheel track can be expressed as:
（6）；
tangential friction can be expressed as:
（7）；
wherein,I rr （t) Is a track irregularity stimulus. The invention adopts the visible-hidden integrated algorithm of VB system. Using a new explicit integration method to expedite the solution of the vehicle-track system; and solving the bridge system by adopting a Newmark-beta implicit integration method.
When a train is running on a bridge that encounters an earthquake, the earthquake ground motion causes vibrations in the bridge abutment through the foundation, which are then transmitted to the train through the bridge's bearings and superstructure. Accordingly, the seismic force may be divided into an inertial force acting on the bridge and an inertial force acting on the train. The equation of motion of the train and the bridge under the action of earthquake can be expressed as follows:
（8）；
（9）；
wherein,F gv ＝andF gb ＝/>seismic forces on trains and bridges are represented as inertial forces, respectively.Is the seismic acceleration vector corresponding to each degree of freedom.
Step 2: and determining the earthquake motion peak acceleration value, the earthquake motion response spectrum characteristic period and the bridge design speed per hour at the bridge position according to the design technical specification of the real large-span cable-stayed railway bridge.
The earthquake motion response spectrum is a functional relationship between the maximum response of the structure and the self-vibration characteristics of the structure under actual earthquake motion.
Step 3: and acquiring enough seismic wave data according to the earthquake design response spectrum, and performing amplitude processing on the seismic wave data according to the peak acceleration value of the earthquake at the bridge position.
The earthquake-proof design reaction spectrum is a reference standard for structural earthquake-proof design, is an idealized earthquake-proof reaction spectrum specified in national standards, and needs to use the characteristic period of the earthquake-proof design reaction spectrum to obtain the earthquake-proof design reaction spectrum.
Step 4: and determining a variation coefficient Cov of the dead weight of the train and the damping ratio of the bridge, and obtaining random parameters through Monte Carlo sampling according to the variation coefficient and the average value.
Step 5: the processed seismic wave data and the self-vibration frequency and vibration mode data of the axle model are input, the fixed parameters and the random parameters of the dead weight of the train and the damping ratio of the bridge are input, and the corresponding data for evaluating the running safety and stability such as the response of the axle coupling system are obtained through calculation.
Step 6: and (3) setting a certain amount of seismic wave data and the determined dead weight and bridge damping ratio parameters of the fixed train as input data, and forming a data set 1 with the corresponding axle coupling system response calculated in the step (5). And (3) setting a certain amount of seismic wave data and the random train dead weight and bridge damping ratio parameters obtained in the step (4) as input data, and forming a data set (2) with the corresponding axle coupling system response obtained in the step (5).
Step 7: and constructing a CNN-Attention-BiGRU deep learning combination network, verifying the prediction correctness of the CNN-Attention-BiGRU deep learning combination network, and performing super-parameter setting on the CNN-Attention-BiGRU deep learning combination network before training by combining actual data.
The CNN-Attention-BiGRU deep learning combination network comprises three modules.
The first module is an encoder module for feature extraction of the time series of seismic data. The module comprises a one-dimensional convolution layer, a LeakyReLU nonlinear mapping layer and a Dropout layer. The one-dimensional convolution layer maps the one-dimensional time sequence to a high-dimensional space, has obtained multi-dimensional features, sets the convolution kernel to 5, the step size to 1, the padding to 2, and the number of channels to 64. The Dropout layer is used to prevent overfitting and set the hidden layer parameter loss rate to 0.5.
The second module is an attention mechanism module, weights the multidimensional features, focuses on the key features, reduces the attention to other information and improves the efficiency and accuracy of task processing. In this block, both the K and Q values are obtained from the output of the encoder, processed through the fully connected layer using tanh as the activation function.
The third module is a decoder module for response prediction of the axle coupling system. The module comprises a BiGRU layer and a full connection layer. The number of channels in the biglu layer is 64. The single-step cyclic output is prone to error accumulation due to the longer length of the final output data. Thus, the algorithm chooses to generate the complete sequence in a direct one-step.
Step 8: and (3) inputting the data set 1 to the CNN-Attention-BiGRU deep learning combination network to carry out prediction training to obtain a prediction model of the dead weight and bridge damping ratio parameters of the deterministic train, and verifying the prediction accuracy of the network under the condition of the deterministic parameters.
Step 9: and (3) inputting the data set 2 into a CNN-Attention-BiGRU deep learning combination network to perform prediction training to obtain a prediction model of the self weight of the uncertainty train and the damping ratio parameters of the bridge, and verifying the prediction accuracy of the network under the condition of the uncertainty parameters.
Step 10: and obtaining more response samples of the axle coupling random vibration system through the CNN-Attention-BiGRU deep learning combination network, and calculating the mean value and standard deviation according to the response samples.
The specific calculation in the CNN-Attention-BiGRU deep learning combination network is as follows:
the one-dimensional convolution layer in the CNN-Attention-BiGRU algorithm can extract features in a one-dimensional time sequence. The computation of the convolution is expressed in matrix form as:
（10）；
wherein,N cov andMconvolution output and input, respectively;Cis a sparse matrix of convolution kernels,representing a convolution operator;bis a bias term.
The Attention mechanism module in the CNN-Attention-BiGRU algorithm further weights the characteristics output by the encoder module, dynamically and adaptively focuses on different parts of the characteristics, and provides better prediction precision for the prediction of the target sequence. The module calculates the similarity between the target output and each element in the input sequence, and obtains the weight of each element. These weights are then used to calculate a weighted sum of the input sequence elements to obtain a weighted sum vector, which is used as the output of the module. The weighted sum vector represents the input sequence, with higher importance to the portion receiving the higher weight. The attention module is shown in fig. 2 and is calculated as follows:
（11）；
wherein,ais the output of the attention mechanism module;his the output of the encoder and the input of the attention mechanism;W v 、W k andW q is a weight matrix of the attention module;K＝hW k is the key vector of the key vector,Q＝hW q is a query vector;V=hW v as a vector of values,as a function of the score,dthe length of the query vector and the key vector;Tto transpose the symbols.
BiGRU in the CNN-Attention-BiGRU algorithm is used for predicting and outputting data. BiGRU is realized by including positive and negative 2 GRU units. The GRU unit has two key components: update gate and reset gate as shown in fig. 3. The reset gate is used to determine how much previous information should be forgotten and irrelevant data can be effectively discarded. The gates are updated to determine how much past state should be preserved and considered, and how to combine new input information with previous state information to help the GRU maintain long-term memory. Update doorz t Reset gater t The following is shown:
（12）；
（13）；
wherein,W z andU z respectively representing the weight matrix learned by the update gate during training and the weight matrix determined at the end of training,W r andU r respectively representing a weight matrix learned by the reset gate during training and a weight matrix determined at the end of training;is a sigmoid function;x t is an input of the current time step,h t-1 is thatt-hidden state of 1 time step;b z in order to update the bias of the gate,b r to reset the bias of the gate.
The reset gate computes the hidden state and the update gate must update the hidden state. The detailed calculation is as follows:
（14）；
（15）；
wherein,is a hyperbolic tangent function, ">Is the Hadamard product, ">Representative timetIs used to update the candidate state of the (c),W h andU h as a matrix of weights that can be learned,b h in order for the offset to be a function of,h t is thattHidden state of time step. The meaning of the remaining parameters is the same as before. When (when)z t Upon convergence to 1, the newly computed candidate hidden state is ignored, which is equivalent to not updating the past state. When (when)z t Upon convergence to 0, the candidate hidden state is preserved. When the sequence has short-term dependencies, the reset gate is in an active state. When the sequence has long-term dependencies, the update gate is active.
Typically, the data at the current time is associated with both the previous time and the future time. On this basis, bigreu obtains bi-directional timing dependencies by stitching 2 GRUs in opposite directions, as shown in fig. 4. This bi-directional structure can help the recurrent neural network extract more information, thereby improving the performance of the learning process. The parameterization formula of biglu is as follows:
（16）；
（17）；
（18）；
wherein,is a hidden state of forward propagation; />Is a hidden state of back propagation and is,α t 、β t andb t respectively weight and bias vectors.
As shown in fig. 5, the proposed CAB neural network architecture includes three modules, including an encoder, an attention module, and a decoder. In a first step, the encoder consists essentially of convolutional layers. Here, the one-dimensional time series maps the convolved layer to a high-dimensional space to obtain the multi-dimensional features. The number of characteristic channels output from the convolutional layer is 64, and the remaining parameters include convolutional kernel 5, step size 1, and fill 2. And secondly, weighting the multidimensional features through an attention module, focusing the key features, reducing the attention to other information and improving the efficiency and accuracy of task processing. In the case of this module, the module,KandQthe values are all obtained from the output of the encoder and are processed by different fully connected layers using tanh as the activation function. In the third step, the decoder consists of a biglu layer and a full-connection layer. The single-step cyclic output is prone to error accumulation due to the longer length of the final output data. Thus, the method selects direct one-step generation of complete sequencesColumns.
To prevent overfitting and obtain better generalization capability, a loss layer with a loss rate of 0.5 is provided in both the encoder and decoder. In addition, the method selects ADAM as the optimizer. Meanwhile, the method sets L2 regularization in an optimizer to further prevent overfitting. During training, the initial learning rate of the optimizer is 0.01. Every 250 epochs, the learning rate scales by a factor of 0.8 until the learning rate drops to 5e-5, and then the change is stopped.
The prediction target of the invention is train safety, including derailment coefficients and the like. Therefore, the method takes the earthquake acceleration as input and takes the train safety as output. The seismic acceleration is normalized before input, the data is mapped into the range of [ -1,1], and the train safety value is not subjected to data preprocessing.
Example verification:
and selecting a steel truss girder double-tower oblique-pull high-speed railway bridge, and comparing the vehicle operation safety with system uncertainty and random near-fault earthquake. The bridge has a full length of 864 meters and a span of 81+135+432+135+81 meters. The overall arrangement of the main bridge is shown in fig. 6. The bridge deck width is 18 meters, two railway lanes are designed, and the center line of the lanes is 2.2 meters away from the center line of the bridge deck. The height of the main beam steel truss beam is 14m. The main tower of the bridge is 180 m in height, and the tower shape is H-shaped. In the numerical model of the bridge, all main beams, piers and main towers are modeled by 3D beam units with 6 degrees of freedom per node, while the tension cables are modeled by 3D rod units with 3 degrees of freedom per node. The damping ratio of the whole bridge structure is set to 0.05.
According to the technical specifications of practical projects, the peak value of the ground vibration acceleration is set to be 0.05g, the characteristic period of the ground vibration response spectrum is set to be 0.35s, and the design speed of the vehicle on the bridge is set to be 200km/h. Derailment coefficients, vehicle lateral and vertical accelerations are used as indicators to evaluate the operational safety of the axle system in near fault earthquakes. German low-disturbance track irregularity random excitation is added in the manufacture of a data set.
(1) Calculation example 1: verifying operation safety of axle system under random near fault earthquake effect
The influence of uncertain parameters is not considered in the calculation example, the weight of the train is 26100kg, and the bridge damping ratio is 0.05. And the results of the CAB model and the biglu-Attention-biglu (BAB) model were compared to show the difference in calculation results of the two models.
100 prepared seismic time series data are calculated by dynamically analyzing an axle system affected by the earthquake so as to obtain the whole captured corresponding train safety time series data. The calculation step length of the earthquake time data and the train safety time data is 0.02. In this case, the filling operation is used to make the seismic time series a uniform length of 20 seconds, and the train safety time series a uniform length of 15.56 seconds according to the time of the train on the bridge. In addition, a ratio of 0.8:0.1:0.1 was chosen, with 80% of the data randomly chosen as the training set, 10% as the test set, and 10% as the validation set.
The method uses the Mean Absolute Error (MAE) as a loss function for predicting the train derailment coefficient. It should be noted that there is a large gap in derailment coefficients affected by different near-fault earthquakes. If the loss function is directly calculated in the training process to obtain prediction data, the loss curve can be greatly fluctuated, and the prediction accuracy is reduced. To alleviate this problem, data processing is required before the loss function is calculated, and the predicted data and the real data are distinguished by the absolute maximum of the real data. The above operation can ensure the stability of the loss curve, thereby improving the prediction accuracy. Fig. 7 (a) and 7 (b) show the loss values at each training stage after the data processing described above, with minimum loss values of 0.0174 and 0.0192, respectively. Notably, the CAB model reaches convergence faster than the BAB model.
Table 1 shows MAE, mean Square Error (MSE) and decision coefficient (R) between all predicted data and corresponding real data in the dataset 2 ) Mean and variance of (c). Here no data processing is performed before calculating the error. Fig. 8 shows a comparison of predicted data with real data. When uncertainty parameters are not taken into account, the error between the two models is not significant. For MAE, the mean of the CAB model is smaller, but the variance is slightly larger. For MSE, CAB model generationThe mean of (c) is slightly larger but the variance is smaller. For R 2 The BAB model is significantly better in both mean and variance.
Table 1 derailment coefficient loss value
。
While these two training models do not take into account the uncertainty parameters of the axle system, they can also be used to strongly predict the data of the uncertainty system. The change of train weight and bridge damping ratio is set in the input layer. The train weight was set at 23941.33 kg and the bridge damping ratio was 0.068. Fig. 9 shows the prediction result, which is less accurate. Therefore, to improve the reliability and accuracy of the proposed method for the predicted response of the uncertain vehicle axle system, it is crucial to integrate the uncertain parameters into the training data set.
(2) Calculation example 2: verification of uncertain axle system operation safety under random near fault earthquake action
Train weight and bridge damping ratio are key factors affecting train safety. To improve the accuracy of the developed model, both parameters were given a coefficient of variation of 0.2, with average train weight 26100kg and bridge damping ratio of 0.05. And adding the response of the corresponding uncertainty axle system as training data. The 30 sets of data are also divided into training, validation and test sets at a ratio of 0.8:0.1:0.1.
MAE was chosen as the loss function and the same data processing was performed after calculation. Fig. 10 (a) and 10 (b) show the loss value for each epoch, with minimum loss values of 0.042 and 0.049, respectively. As with example 1, CAB model can reach convergence faster than BAB model.
Table 2 gives the mean and variance of MAE, MSE and R2 for all predicted data relative to the corresponding actual data in the dataset. FIG. 11 shows a comparison of one generated data versus actual data based on the same seismic time series of FIG. 8. When the uncertain parameters are considered, the data generated by the CAB model has a smaller average value in terms of average absolute error and mean square error. But for variance, the results of the BAB model are significantly smaller. In addition, the mean value of R2 of the CAB model is significantly better than that of the BAB model, and the mean values of R2 are 0.93866 and 0.82829 respectively. This shows that the CAB model is more advantageous, especially when considering uncertainty in key parameters such as train weight and bridge damping ratio.
Table 2 derailment coefficient loss value
。
In summary, the CNN-Attention-BiGRU model proposed by the invention aims to predict the running safety of trains on bridges during Near Fault Earthquakes (NFEs). The model adopts a CNN module to effectively extract characteristics from input data, utilizes a BiGRU module to predict and output train safety coefficients, and uses an Attention module to accurately position and emphasize key characteristics most relevant to output data. Through practical calculation, the prediction accuracy of the CAB model and the BAB model is relatively similar under the condition that the uncertainty of the train weight and the bridge damping ratio is not considered. However, the CAB model shows higher prediction accuracy when considering uncertainty in train weight and bridge damping ratio. In addition, the CAB model converges faster than the BAB model, indicating that it has higher efficiency under adaptive and accurately predictive variable conditions.

Claims (3)

1. The earthquake-vehicle-bridge system random vibration analysis method based on deep learning is characterized by comprising the following steps of:
step 1: establishing a train model and a bridge model, extracting self-vibration frequency and vibration mode data of the train model and the bridge model, and verifying the correctness of the bridge model through data obtained by analysis and calculation;
step 2: according to the design technical specification of a real large-span cable-stayed railway bridge, determining a seismic peak acceleration value, a seismic response spectrum characteristic period and a bridge design speed per hour at a bridge position;
step 3: acquiring seismic wave data according to a seismic design response spectrum, and performing amplitude processing on the seismic wave data according to a seismic vibration peak acceleration value at a bridge position;
step 4: determining a variation coefficient Cov of the self-weight of the train and the damping ratio of the bridge, and obtaining random parameters of the self-weight of the train and the damping ratio of the bridge through Monte Carlo sampling according to the variation coefficient and the average value;
step 5: according to the processed seismic wave data, the self-vibration frequency and vibration mode data of the axle model, and the fixed parameters and the random parameters of the determined dead weight of the train and the damping ratio of the bridge, calculating to obtain the response of the corresponding axle coupling system, and evaluating the operation safety and stability;
step 6: setting fixed parameters of the set number of seismic wave data and the determined dead weight of the train and the bridge damping ratio as input data, and forming a data set 1 with the corresponding axle coupling system response calculated in the step 5; setting the set number of seismic wave data and random parameters of the dead weight of the train and the damping ratio of the bridge obtained in the step 4 as input data, and forming a data set 2 with the response of the corresponding axle coupling system calculated in the step 5;
step 7: constructing a CNN-Attention-BiGRU deep learning combination network, verifying the prediction correctness of the CNN-Attention-BiGRU deep learning combination network, and performing super-parameter setting on the CNN-Attention-BiGRU deep learning combination network before training by combining actual data;
step 8: inputting the data set 1 into a CNN-Attention-BiGRU deep learning combination network for prediction training to obtain a prediction model of deterministic train dead weight and bridge damping ratio parameters, and verifying the prediction accuracy of the network under deterministic parameter conditions;
step 9: inputting the data set 2 into a CNN-Attention-BiGRU deep learning combination network for prediction training to obtain a prediction model of the self weight of the uncertain train and the damping ratio parameters of the bridge, and verifying the prediction accuracy of the network under the condition of the uncertain parameters;
step 10: and obtaining more response samples of the axle coupling random vibration system through the CNN-Attention-BiGRU deep learning combination network, and calculating the mean value and standard deviation according to the response samples.
2. The deep learning based random vibration analysis method of a seismic-car-bridge system according to claim 1, wherein the CNN-Attention-biglu deep learning combined network comprises three modules: an encoder module, an attention mechanism module, and a decoder module; the method comprises the following steps:
the encoder module is used for extracting the characteristics of the seismic data time sequence and comprises a one-dimensional convolution layer, a LeakyReLU nonlinear mapping layer and a Dropout layer; mapping the one-dimensional time sequence to a high-dimensional space by the one-dimensional convolution layer to obtain multi-dimensional characteristics; the Dropout layer is used for preventing overfitting;
the attention mechanism module is used for weighting the multidimensional features, focusing on the key features and reducing the attention to other information so as to improve the efficiency and accuracy of task processing;
the decoder module is used for predicting the response of the axle coupling system and comprises a BiGRU layer and a full-connection layer;
the algorithm employs a direct one-step generation of the complete sequence.
3. The deep learning-based random vibration analysis method of the earthquake-vehicle-bridge system according to claim 2, wherein the specific calculation in the CNN-Attention-biglu deep learning combination network is as follows:
the one-dimensional convolution layer in the encoder module extracts features in a one-dimensional time sequence, and the calculation of convolution is expressed as a matrix form:
（1）；
wherein,N cov andMconvolution output and input, respectively;Cis a sparse matrix of convolution kernels,representing a convolution operator;bis a bias term;
the attention mechanism module further weights the characteristics output by the encoder module, dynamically and adaptively focuses on different parts of the characteristics, and provides better prediction precision for the prediction of the target sequence; the attention mechanism module calculates the similarity between each element in the target output and input sequence, and obtains the weight of each element; then using these weights to calculate a weighted sum of the input sequence elements to obtain a weighted sum vector, which is taken as the output of the attention mechanism module; the calculation is as follows:
（2）；
wherein,ais the output of the attention mechanism module;his the output of the encoder and the input of the attention mechanism;W v 、W k andW q is a weight matrix of the attention module;K＝hW k is the key vector of the key vector,Q＝hW q is a query vector;V=hW v as a vector of values,as a function of the score,dthe length of the query vector and the key vector;Ttranspose the symbol;
the BiGRU in the CNN-Attention-BiGRU algorithm is used for predicting and outputting data; the biglu comprises a front and back 2 GRU units, which include two key components: an update gate to determine how much past state should be preserved and considered, and how to combine new input information with previous state information to help the GRU maintain long term memory; the reset gate is used to determine how much previous information should be forgotten and can effectively discard irrelevant data; update doorz t Reset gater t The following is shown:
（3）；
（4）；
wherein,W z andU z respectively representing the weight matrix learned by the update gate during training and the weight matrix determined at the end of training,W r andU r respectively representing a weight matrix learned by the reset gate during training and a weight matrix determined at the end of training;is a sigmoid function;x t is an input of the current time step,h t-1 is thatt-hidden state of 1 time step;b z in order to update the bias of the gate,b r bias for reset gate;
the reset gate calculates the hidden state, and the update gate updates the hidden state; the detailed calculation is as follows:
（5）；
（6）；
wherein,is a hyperbolic tangent function, ">Is the Hadamard product, ">An update candidate state representing time t;W h andU h as a matrix of weights that can be learned,b h in order for the offset to be a function of,h t is thattA hidden state of the time step;
when (when)z t Upon convergence to 1, the newly computed candidate hidden stateIf the state is ignored, the past state is not updated; when (when)z t When converging to 0, the candidate hidden state is preserved; when the sequence has short-term dependency, the reset gate is in an active state; when the sequence has long-term dependence, the update gate is in an active state;
BiGRU obtains two-way timing dependencies by concatenating 2 GRUs in opposite directions, and the parameterized formula for BiGRU is as follows:
（7）；
（8）；
（9）；
wherein,is a hidden state of forward propagation, +.>Is a hidden state of back propagation and is,α t andβ t the weights of the forward propagating hidden state and the backward propagating hidden state respectively,b t is a bias vector.
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