A method and system for evaluating the nonlinear restoring force of bridge bearing structures based on hybrid deep learning

Abstract

The present invention discloses a method and system for evaluating the nonlinear restoring force of a bridge support structure based on hybrid deep learning. First, a vehicle multi-rigid body dynamics model, a nonlinear finite element model of a track-bridge structure under earthquakes, and a wheel-rail contact model are constructed. Then, the vehicle multi-rigid body dynamics model, the nonlinear finite element model of a track-bridge structure under earthquakes, and the wheel-rail contact model are combined into an earthquake vehicle-bridge model based on structural nonlinear restoring force. The present invention realizes the function of directly simulating the support structure relationship by using earthquake motion input, thereby further simulating the support restoring force and quickly and accurately evaluating the nonlinear restoring force of the train-track-bridge. In addition, when the train model enters the bridge, positive transverse and vertical seismic waves are loaded until the train leaves the bridge, thereby obtaining the longitudinal-transverse restoring force of the supports at each position and the earthquake-tectonic seismic restoring force, and is suitable for wide promotion and use.

Description

Technical Field

[0001] The present invention relates to the technical field of nonlinear restoring force evaluation of bridge bearing structures, and in particular to a method and system for nonlinear restoring force evaluation of bridge bearing structures based on hybrid deep learning. Background Art

[0002] The nonlinear restoring force of a bridge bearing structure refers to the nonlinear mechanical properties exhibited during the deformation and recovery process of the bearing after being subjected to external forces. Bridge bearings are critical components connecting the bridge superstructure and substructure, responsible for reliably transmitting the reaction forces and deformations of the superstructure to the substructure. However, under extreme conditions such as earthquakes, the stresses acting on the bearings become complex, and their restoring force no longer exhibits a simple linear relationship, but rather exhibits nonlinear behavior.

[0003] At present, under the action of earthquakes, most track-bridge structures will enter different degrees of plastic failure. In addition, due to the large overall stiffness of high-speed railway track-bridge structures, the main nonlinear form of high-speed railway track-bridge structures is material elastic-plastic, and it is less likely to cause structural failure caused by geometric nonlinearity. The evaluation process of existing bridge support structure nonlinear restoring force evaluation methods generally has low computational efficiency, resulting in a large amount of evaluation time being consumed during the evaluation process. Not only are the evaluation results less accurate and reliable, but there is also a serious safety hazard of misjudging bridge damage. Therefore, it is necessary to design a bridge support structure nonlinear restoring force evaluation method and system based on hybrid deep learning. Summary of the Invention

[0004] The purpose of the present invention is to overcome the shortcomings of the prior art and to better and effectively solve the problem that the evaluation process of the existing bridge support structure nonlinear restoring force evaluation method has low computational efficiency, which results in a large amount of evaluation time being consumed in the evaluation process. Not only are the evaluation results of low accuracy and poor reliability, but there are also serious safety hazards of misjudgment of bridge damage. A bridge support structure nonlinear restoring force evaluation method and system based on hybrid deep learning is provided, which realizes the function of directly simulating the support structure relationship by using seismic input to further simulate the support restoring force and quickly and accurately perform nonlinear restoring force evaluation of the train-track-bridge, and loads positive transverse and vertical seismic waves when the train model enters the bridge until the train leaves the bridge, thereby obtaining the longitudinal-transverse restoring force of the support at each position and the seismic structural seismic-restoring force.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] A method and system for evaluating the nonlinear restoring force of a bridge support structure based on hybrid deep learning, comprising the following steps:

[0007] Step A: construct a vehicle multi-rigid body dynamics model, a nonlinear finite element model of the track-bridge structure under earthquake conditions, and a wheel-rail contact model. These models are then combined into a seismic vehicle-bridge model based on structural nonlinear restoring force.

[0008] Step B: Based on the earthquake vehicle-bridge model, a temporal evaluation network TAB is established that integrates the temporal convolutional network (TCN), the self-attention mechanism (SA), and the bidirectional long short-term memory (BiLSTM) network to obtain the physical mapping relationship between ground motion and nonlinear restoring force.

[0009] Step C: Evaluate the nonlinear restoring force of the bearing structure based on the physical mapping relationship between earthquake motion and nonlinear restoring force, and complete the nonlinear restoring force evaluation operation of the bridge bearing structure.

[0010] The aforementioned hybrid deep learning-based bridge support structure nonlinear restoring force evaluation method includes step A, which constructs a vehicle multi-rigid body dynamics model, a nonlinear finite element model of the track-bridge structure under earthquakes, and a wheel-rail contact model. The vehicle multi-rigid body dynamics model, the nonlinear finite element model of the track-bridge structure under earthquakes, and the wheel-rail contact model are then combined into an earthquake vehicle-bridge model based on structural nonlinear restoring force. The specific steps are as follows:

[0011] Step A1: Construct a multi-rigid body dynamics model of the vehicle, where the motion equation of a single rigid body is expressed as shown in formula (1) and formula (2).

[0012]

[0013] Among them, m i is the mass of the i-th rigid body, I is the unit matrix, J i is the principal inertia tensor of the center of the i-th rigid body, F i and M i are the principal vector and principal moment of the suspension force and contact force related to the absolute coordinate system, ω i is the projection of the instantaneous angular velocity vector in the absolute coordinate system;

[0014] Step A2: Construct a nonlinear finite element model of the track-bridge structure under earthquake conditions. The specific steps are as follows:

[0015] Step A21: Based on Hamilton's principle, the motion equation of the track-bridge structure is established, as shown in formula (3):

[0016]

[0017] Among them, [M TB ]、[C TB ] and [K TB] are the mass matrix, damping matrix and stiffness matrix of the track-bridge structure system, respectively. con} represents the equivalent nodal load vector of the contact between wheelset and rail, {F g} represents the vector of external additional loads such as earthquake load and gravity;

[0018] Step A22, describe the material nonlinearity of the structure by macroscopic component internal force-deformation to establish a restoring force model, as shown in formula (4),

[0019]

[0020] Where x is the deformation of the component and g is the hysteretic restoring force;

[0021] Step A23, decompose the hysteresis restoring force g into the sum of the elastic force and the hysteresis force, as shown in formula (5),

[0022]

[0023] Among them, αkx is the elastic force part, z is the hysteresis displacement;

[0024] Step A24, solve the hysteresis displacement z, as shown in formula (6),

[0025]

[0026] Among them, ε() is the unit step function, x y is the yield displacement of the component;

[0027] In step A25, a nonlinear finite element model of the track-bridge structure of key components is established using the local nonlinear force updating technology, thereby obtaining the corrected nonlinear track-bridge structure motion equation as shown in formula (7):

[0028]

[0029] Among them, {F K} and {F C} are load correction terms caused by structural stiffness and damping nonlinearity respectively;

[0030] Step A26, set the earthquake acceleration to The motion equation of the track-bridge under earthquake is shown in formula (8):

[0031]

[0032] Step A3: constructing a wheel-rail contact model, wherein the wheel-rail contact model includes wheel-rail contact position search and wheel-rail contact force calculation. The specific steps are as follows:

[0033] Step A31, searching for the wheel-rail contact position, wherein the wheel-rail contact is determined using the trace method;

[0034] Step A32, wheel-rail contact force calculation, specifically using Hertz nonlinear spring to update the wheel-rail contact normal force, and then using Kalker theory to calculate the tangential creep force.

[0035] The aforementioned hybrid deep learning-based bridge support structure nonlinear restoring force evaluation method, step B, based on the earthquake vehicle-bridge model, establishes a temporal evaluation network TAB that integrates the time convolution network TCN, the self-attention mechanism SA, and the bidirectional long short-term memory network BiLSTM to obtain the physical mapping relationship between earthquake motion and nonlinear restoring force. The specific steps are as follows:

[0036] Step B1, constructing a temporal convolutional network (TCN), wherein the temporal convolutional network (TCN) is used to capture multivariate time series information, and the temporal convolutional network (TCN) is composed of dilated causal convolution (DCC);

[0037] Step B2: establishing a self-attention mechanism SA, which is used to simultaneously process the correlation of different parts of the entire sequence data and make the calculation process highly parallel;

[0038] Step B3, construct a bidirectional long short-term memory network BiLSTM, which is used to further optimize the model's processing ability for time series data and simultaneously consider the forward and backward information of the time series to improve the model evaluation accuracy. The bidirectional long short-term memory network BiLSTM specifically uses memory units to store long-term historical information, and then selectively retains and updates the information through a forget gate, an input gate, and an output gate. The forget gate is used to selectively discard long-term memory, the input gate is used to update long-term memory, and the output gate is used to combine short-term memory and long-term memory to output the current moment result.

[0039] The aforementioned method for evaluating the nonlinear restoring force of a bridge support structure based on hybrid deep learning, step B1 specifically includes the following steps:

[0040] Step B11, construct the dilated causal convolution DCC, where the input time series of the dilated causal convolution DCC is x∈R n , and the filter is f:{1,2,...,k-1}, then the dilated convolution operation F(s) on the element s in the one-dimensional sequence is as shown in formula (9),

[0041]

[0042] Where k is the size of the filter, w(j) is the weight of the convolution kernel, and * is the convolution operation;

[0043] Step B12: Adjust the expansion factor to expand the receptive field R of the temporal convolutional network TCN field , as shown in formula (10),

[0044] R field =K·(N stack -1)·d i +1 (10)

[0045] Among them, d i is the expansion factor;

[0046] Step B13, construct a causal expansion convolution residual module, which is composed of two groups of causal expansion convolution layers, weight normalization layers, activation functions ReLU and Dropout layers connected in sequence from bottom to top. The input features of the causal expansion convolution residual module pass through the first layer of causal expansion convolution layer, normalization layer, activation function ReLU and Dropout layer in sequence to obtain output features, and then use the output features of the previous layer as the input features of the second layer of causal expansion convolution, and then pass through the second layer of normalization layer, activation function ReLU and Dropout layer in sequence to obtain output features. If the input dimension and output dimension are different, 1×1 convolution is used as the cross-path layer to ensure the dimension matching of the feature matrix.

[0047] The aforementioned method for evaluating the nonlinear restoring force of bridge bearing structures based on hybrid deep learning, step B2 specifically includes the following steps:

[0048] Step B21, for input feature X={x1,x2,…,x T} is matrixed as shown in formula (11),

[0049]

[0050] in, To optimize the scaling factor of training, Q is Query, and K is the key, and V is Value, and

[0051] Step B22, expands the attention to local features at multiple locations. Specifically, the input sequence is first divided into blocks of fixed size, and then the Query, Key, and Value in each block are projected with different linear transformations. Then, attention is calculated in parallel on each block. After the calculation, the attention results of each block are spliced ​​and combined through linear transformation. The independent scaled dot product attention calculations will be integrated by linear transformation to obtain the final output value, as shown in formulas (12) and (13).

[0052] MultiHead(Q,K,V)=Concatenate(head1,…,head h )W o (12)

[0053] head i =Attention(QW i Q ,LW i K ,VW i V ) (13)

[0054] in, and are all self-attention weights, is the multi-head attention weight, and Concatenate is the concatenation operation.

[0055] The aforementioned method for evaluating the nonlinear restoring force of a bridge support structure based on hybrid deep learning, step B3 specifically includes the following steps:

[0056] Step B31, set the earthquake input to I t , the cell state C at the previous moment t-1 , hidden layer output data h t-1 and the current input data I t Input cell and update forget gate f t and input gate i t , and then according to the initial memory cell parameters And the memory cell parameter C passed at the previous moment t-1 Update and obtain the final memory parameter C at the current moment t , and the output gate O t Use the final memory parameter C at the current moment t Derive and update the previous hidden state h at each time step t , and then the current memory parameter C t With the current hidden layer state h t Enter the next moment, the specific process is shown in formula (14),

[0057] i t =σ(W i ·[h t-1 ,I t ]+b i ), f t =σ(W f ·[h t-1 ,I t ]+b f ),

[0058] O t =σ(W O ·[h t-1 ,I t ]+b O ), h t =O t ⊙tanh(C t );

[0059]

[0060] Where σ is the sigmoid activation function, tanh is the hyperbolic tangent activation function, ⊙ is the dot product operation; W and b are the weights and biases of various gates respectively;

[0061] Step B32: Add time flow data information from the future to the past to mine the forward and backward dependencies of the time series, and reverse LSTM B and forward LSTM F As shown in formulas (15) and (16),

[0062]

[0063] The arrows indicate the direction of information flow. t Input data for the time history of seismic waves, Out t is the final output of the earthquake response at the corresponding moment,

[0064] Step B33, LSTM B and LSTM F are the forward and backward iterations of the LSTM hidden state at different times, as shown in formula (17),

[0065]

[0066] in, To sum by weight;

[0067] Step B4: Establish a temporal evaluation network TAB that integrates the temporal convolutional network TCN, the self-attention mechanism SA, and the bidirectional long short-term memory network BiLSTM. The temporal evaluation network TAB uses Huber Loss as the loss function, as shown in formula (18).

[0068]

[0069] Among them, Y j is the evaluation value, T j is the true value, δ is the adjustment coefficient; if |Y j -T j When |≤δ, the loss function lossj is a quadratic function; if |Y j -T j |>δ, the loss function is in the form of a linear function.

[0070] The aforementioned method for evaluating the nonlinear restoring force of a bridge support structure based on hybrid deep learning, step C, evaluates the nonlinear restoring force of the support structure according to the physical mapping relationship between seismic motion and nonlinear restoring force, and completes the evaluation of the nonlinear restoring force of the bridge support structure. Specifically, the mean absolute error (MAE), the root mean square error (RMSE), and the coefficient of determination (R) are used to calculate the nonlinear restoring force. 2 The nonlinear restoring force of the support structure is evaluated, as shown in formula (19),

[0071]

[0072] Where Ω is the sample size, Y j is the evaluation value, T j is the true value, is the true mean value.

[0073] A nonlinear restoring force evaluation system for bridge bearing structures based on hybrid deep learning includes an earthquake vehicle-bridge model construction module, a restoring force physical mapping relationship acquisition module, and a support structure nonlinear restoring force evaluation module. The earthquake vehicle-bridge model construction module is used to construct a vehicle multi-rigid body dynamics model, a track-bridge structure nonlinear finite element model under earthquakes, and a wheel-rail contact model, and then combine the vehicle multi-rigid body dynamics model, the track-bridge structure nonlinear finite element model under earthquakes, and the wheel-rail contact model into a earthquake vehicle-bridge model based on structural nonlinear restoring force; the restoring force physical mapping relationship acquisition module is used to establish a temporal evaluation network TAB that integrates a time convolutional network TCN, a self-attention mechanism SA, and a bidirectional long short-term memory network BiLSTM based on the earthquake vehicle-bridge model and obtain a seismic motion-nonlinear restoring force physical mapping relationship; the support structure nonlinear restoring force evaluation module is used to evaluate the nonlinear restoring force of the support structure according to the seismic motion-nonlinear restoring force physical mapping relationship and complete the bridge support structure nonlinear restoring force evaluation operation.

[0074] The beneficial effects of the present invention are as follows: a method and system for evaluating the nonlinear restoring force of a bridge support structure based on hybrid deep learning of the present invention first constructs a vehicle multi-rigid body dynamics model, a nonlinear finite element model of a track-bridge structure under an earthquake, and a wheel-rail contact model, and then combines the vehicle multi-rigid body dynamics model, the nonlinear finite element model of a track-bridge structure under an earthquake, and the wheel-rail contact model into an earthquake vehicle-bridge model based on structural nonlinear restoring force, and then establishes a temporal evaluation network TAB that integrates a time convolutional network TCN, a self-attention mechanism SA, and a bidirectional long short-term memory network BiLSTM based on the earthquake vehicle-bridge model and obtains a physical mapping relationship between earthquake motion and nonlinear restoring force, and then evaluates the nonlinear restoring force of the support structure according to the physical mapping relationship between earthquake motion and nonlinear restoring force and completes the evaluation operation of the nonlinear restoring force of the bridge support structure; it effectively realizes that the nonlinear restoring force evaluation method and system of the bridge support structure has the characteristics of adopting earthquake motion input directly to evaluate the nonlinear restoring force of the bridge support structure. It simulates the structural relationship of the support to further simulate the support restoring force and quickly and accurately evaluate the nonlinear restoring force of the train-track-bridge. When the train model enters the bridge, positive transverse and vertical seismic waves are loaded until the train leaves the bridge, thereby obtaining the longitudinal-transverse restoring force of the support at each position and the seismic-tectonic seismic-restoring force. At the same time, the time convolution network TCN can effectively capture multivariate time series information, and the self-attention mechanism SA solves the problem that the fully connected neural network cannot establish associations for multiple related inputs. The self-attention mechanism SA can simultaneously process the correlation between different parts of the entire sequence data, thereby achieving a high degree of parallelization of the calculation process, and then effectively capture the global contextual relationship and model the long-term dependency relationship with obvious effect. The bidirectional long short-term memory network BiLSTM can further optimize the model's processing ability for time series data and simultaneously consider the forward and backward information of the time series to improve the model evaluation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 It is a flow chart of a method and system for evaluating the nonlinear restoring force of a bridge bearing structure based on hybrid deep learning of the present invention;

[0076] Figure 2 1 is a comparison chart of the prediction accuracy and PSD of the nonlinear restoring force of the support under different earthquake motions in the embodiment of the present invention. DETAILED DESCRIPTION

[0077] The present invention will be further described below with reference to the accompanying drawings.

[0078] like Figure 1 As shown, the present invention provides a method and system for evaluating the nonlinear restoring force of a bridge support structure based on hybrid deep learning, comprising the following steps:

[0079] Step A: Construct a vehicle multi-rigid body dynamics model, a nonlinear finite element model of the track-bridge structure under earthquake conditions, and a wheel-rail contact model. Then, these models are combined into a seismic vehicle-bridge model based on structural nonlinear restoring force. The specific steps are as follows:

[0080] Step A1: Construct a multi-rigid body dynamics model of the vehicle, where the motion equation of a single rigid body is expressed as shown in formula (1) and formula (2).

[0081]

[0082]

[0083] Among them, m i is the mass of the i-th rigid body, I is the unit matrix, J i is the principal inertia tensor of the center of the i-th rigid body, F i and M i are the principal vector and principal moment of the suspension force and contact force related to the absolute coordinate system, ω i is the projection of the instantaneous angular velocity vector in the absolute coordinate system;

[0084] Step A2: Construct a nonlinear finite element model of the track-bridge structure under earthquake conditions. The specific steps are as follows:

[0085] Step A21: Based on Hamilton's principle, the motion equation of the track-bridge structure is established, as shown in formula (3):

[0086]

[0087] Among them, [M TB ]、[C TB ] and [K TB ] are the mass matrix, damping matrix and stiffness matrix of the track-bridge structure system, respectively. con} represents the equivalent nodal load vector of the contact between wheelset and rail, {F g} represents the vector of external additional loads such as earthquake load and gravity;

[0088] Step A22, describe the material nonlinearity of the structure by macroscopic component internal force-deformation to establish a restoring force model, as shown in formula (4),

[0089]

[0090] Where x is the deformation of the component and g is the hysteretic restoring force;

[0091] Step A23, decompose the hysteresis restoring force g into the sum of the elastic force and the hysteresis force, as shown in formula (5),

[0092]

[0093] Among them, αkx is the elastic force part, z is the hysteresis displacement;

[0094] Step A24, solve the hysteresis displacement z, as shown in formula (6),

[0095]

[0096] Among them, ε() is the unit step function, x y is the yield displacement of the component;

[0097] In step A25, a nonlinear finite element model of the track-bridge structure of key components is established using the local nonlinear force updating technology, thereby obtaining the corrected nonlinear track-bridge structure motion equation as shown in formula (7):

[0098]

[0099] Among them, {F K} and {F C} are load correction terms caused by structural stiffness and damping nonlinearity respectively;

[0100] Step A26, set the earthquake acceleration to The motion equation of the track-bridge under earthquake is shown in formula (8):

[0101]

[0102] Step A3: constructing a wheel-rail contact model, wherein the wheel-rail contact model includes wheel-rail contact position search and wheel-rail contact force calculation. The specific steps are as follows:

[0103] Step A31, searching for the wheel-rail contact position, wherein the wheel-rail contact is determined using the trace method;

[0104] Step A32, wheel-rail contact force calculation, specifically using Hertz nonlinear spring to update the wheel-rail contact normal force, and then using Kalker theory to calculate the tangential creep force.

[0105] Step B: Based on the earthquake bridge model, a temporal evaluation network TAB is established that integrates the temporal convolutional network TCN, the self-attention mechanism SA, and the bidirectional long short-term memory network BiLSTM to obtain the physical mapping relationship between earthquake motion and nonlinear restoring force. The specific steps are as follows:

[0106] Step B1: construct a temporal convolutional network (TCN). The temporal convolutional network (TCN) is used to capture multivariate time series information. The temporal convolutional network (TCN) is composed of dilated causal convolution (DCC). The specific steps are as follows:

[0107] Step B11, construct the dilated causal convolution DCC, where the input time series of the dilated causal convolution DCC is x∈R n , and the filter is f:{1,2,...,k-1}, then the dilated convolution operation F(s) on the element s in the one-dimensional sequence is as shown in formula (9),

[0108]

[0109] Where k is the size of the filter, w(j) is the weight of the convolution kernel, and * is the convolution operation;

[0110] Step B12: Adjust the expansion factor to expand the receptive field R of the temporal convolutional network TCN field , as shown in formula (10),

[0111] R field =K·(N stack -1)·d i +1 (10)

[0112] Among them, d i is the expansion factor;

[0113] Step B13: construct a causal expansion convolution residual module, which is composed of two groups of causal expansion convolution layers, weight normalization layers, activation functions ReLU, and Dropout layers connected in sequence from bottom to top. The input features of the causal expansion convolution residual module are sequentially passed through the first layer of causal expansion convolution layer, normalization layer, activation function ReLU, and Dropout layer to obtain output features. The output features of the previous layer are then used as the input features of the second layer of causal expansion convolution, and then sequentially passed through the second layer of normalization layer, activation function ReLU, and Dropout layer to obtain output features. If the input dimension and output dimension are different, a 1×1 convolution is used as the cross-path layer to ensure dimensional matching of the feature matrix.

[0114] Step B2: Establish a self-attention mechanism SA, which is used to simultaneously process the correlation of different parts of the entire sequence data and make the calculation process highly parallel. The specific steps are as follows:

[0115] Step B21, for input feature X={x1,x2,…,x T} is matrixed as shown in formula (11),

[0116]

[0117] in, To optimize the scaling factor of training, Q is Query, and K is the key, and V is Value, and

[0118] Step B22, expands the attention to local features at multiple locations. Specifically, the input sequence is first divided into blocks of fixed size, and then the Query, Key, and Value in each block are projected with different linear transformations. Then, attention is calculated in parallel on each block. After the calculation, the attention results of each block are spliced ​​and combined through linear transformation. The independent scaled dot product attention calculations will be integrated by linear transformation to obtain the final output value, as shown in formulas (12) and (13).

[0119] MultiHead(Q,K,V)=COncatenate(head1,…,head h )W o (12)

[0120] head i =Attention(QW i Q ,KW i K ,VW i V ) (13)

[0121] in, and are all self-attention weights, is the multi-head attention weight, and Concatenate is the concatenation operation;

[0122] Step B3, construct a bidirectional long short-term memory network BiLSTM, the bidirectional long short-term memory network BiLSTM is used to further optimize the model's processing ability for time series data and simultaneously consider the forward and backward information of the time series to improve the model evaluation accuracy. The bidirectional long short-term memory network BiLSTM specifically uses memory units to store long-term historical information, and then selectively retains and updates the information through a forget gate, an input gate, and an output gate. The forget gate is used to selectively discard long-term memory, the input gate is used to update long-term memory, and the output gate is used to combine short-term memory and long-term memory to output the current moment result. The specific steps are as follows:

[0123] Step B31, set the earthquake input to I t , the cell state C at the previous moment t-1 , hidden layer output data h t-1 and the current input data I t Input cell and update forget gate f t and input gate i t, and then according to the initial memory cell parameters And the memory cell parameter C passed at the previous moment t-1 Update and obtain the final memory parameter C at the current moment t , and the output gate O t Use the final memory parameter C at the current moment t Derive and update the previous hidden state h at each time step t , and then the current memory parameter C t With the current hidden layer state h t Enter the next moment, the specific process is shown in formula (14),

[0124] i t =σ(W i ·[h t-1 ,I t ]+b i ), f t =σ(W f ·[h t-1 ,I t ]+b f ),

[0125] O t =σ(W O ·[h t-1 ,I t ]+b O ), h t =O t ⊙tanh(C t );

[0126]

[0127] Where σ is the sigmoid activation function, tanh is the hyperbolic tangent activation function, ⊙ is the dot product operation; W and b are the weights and biases of various gates respectively;

[0128] Step B32: Add time flow data information from the future to the past to mine the forward and backward dependencies of the time series, and reverse LSTM B and forward LSTM F As shown in formulas (15) and (16),

[0129]

[0130] The arrows indicate the direction of information flow. t Input data for the time history of seismic waves, Out t is the final output of the earthquake response at the corresponding moment,

[0131] Step B33, LSTM B and LSTM F are the forward and backward iterations of the LSTM hidden state at different times, as shown in formula (17),

[0132]

[0133] in, To sum by weight;

[0134] Step B4: Establish a temporal evaluation network TAB that integrates the temporal convolutional network TCN, the self-attention mechanism SA, and the bidirectional long short-term memory network BiLSTM. The temporal evaluation network TAB uses Huber Loss as the loss function, as shown in formula (18).

[0135]

[0136] Among them, Y j is the evaluation value, T j is the true value, δ is the adjustment coefficient; if |Y j -T j When |≤δ, the loss function loss j is a quadratic function; if |Y j -T j |>δ, the loss function is in the form of a linear function.

[0137] Step C: evaluate the nonlinear restoring force of the support structure according to the physical mapping relationship between earthquake motion and nonlinear restoring force, and complete the evaluation of the nonlinear restoring force of the bridge support structure. Specifically, the mean absolute error (MAE), root mean square error (RMSE) and determination coefficient (R) are used to calculate the nonlinear restoring force of the support structure. 2 The nonlinear restoring force of the support structure is evaluated, as shown in formula (19),

[0138]

[0139] Where Ω is the sample size, Y j is the evaluation value, T j is the true value, is the true mean value.

[0140] A nonlinear restoring force evaluation system for bridge bearing structures based on hybrid deep learning includes an earthquake vehicle-bridge model construction module, a restoring force physical mapping relationship acquisition module, and a support structure nonlinear restoring force evaluation module. The earthquake vehicle-bridge model construction module is used to construct a vehicle multi-rigid body dynamics model, a track-bridge structure nonlinear finite element model under earthquakes, and a wheel-rail contact model, and then combine the vehicle multi-rigid body dynamics model, the track-bridge structure nonlinear finite element model under earthquakes, and the wheel-rail contact model into a earthquake vehicle-bridge model based on structural nonlinear restoring force; the restoring force physical mapping relationship acquisition module is used to establish a temporal evaluation network TAB that integrates a time convolutional network TCN, a self-attention mechanism SA, and a bidirectional long short-term memory network BiLSTM based on the earthquake vehicle-bridge model and obtain a seismic motion-nonlinear restoring force physical mapping relationship; the support structure nonlinear restoring force evaluation module is used to evaluate the nonlinear restoring force of the support structure according to the seismic motion-nonlinear restoring force physical mapping relationship and complete the bridge support structure nonlinear restoring force evaluation operation.

[0141] To better illustrate the effectiveness of the present invention, the following describes a specific embodiment of the present invention. The dataset was divided into 60% training, 20% validation, and 20% test sets. The data was randomly shuffled before training to ensure fair comparison of evaluation results. The network for this embodiment was implemented using MATLAB, and the evaluation model was trained on an NVIDIA GTX3090 GPU. The model was trained for 200 epochs, using a batch size of 128 and the Adam optimizer with an initial learning rate of 0.01. To enhance convergence, the learning rate was gradient descent, with a 25% decrease every 10 epochs. Weights were initialized with a standard Gaussian distribution, with a base filterSize of 3, numFilters of 128, and a dropoutFactor of 0.2. The data was shuffled after each epoch, and the network was validated every 10 epochs. This embodiment used an early stopping strategy and L2 regularization to prevent overfitting. Early stopping was set to stop after 20 epochs if there was no significant improvement in accuracy. The L2 regularization value was set to 0.001.

[0142] like Figure 2 The figure shows the comparison of the prediction accuracy and PSD of the nonlinear restoring force of the support under different earthquake motions. It can be seen from the figure that the model proposed in the present invention can effectively predict the nonlinear restoring force of the support, and has significant prediction accuracy in both time domain and frequency domain. At the same time, the evaluation accuracy under different earthquakes is not much different. The present invention has significant advantages in evaluation stability.

[0143] Table 1. Evaluation results of different span support accuracy

[0144]

[0145] Table 1 shows the evaluation results for the accuracy of supports with different spans. As can be seen from Table 1, the proposed TAB network exhibits excellent performance for both fixed and sliding supports with different spans. The R2 values ​​are all greater than 90%, with those for the sliding support with span 1 and the fixed support with span 3 exceeding 99%. This demonstrates the network's significant advantages in data interpretation, fitting capabilities, model accuracy, and reliability.

[0146] In summary, the present invention provides a method and system for evaluating the nonlinear restoring force of a bridge support structure based on hybrid deep learning. First, a vehicle multi-rigid body dynamics model, a nonlinear finite element model of a track-bridge structure under an earthquake, and a wheel-rail contact model are constructed. Then, the vehicle multi-rigid body dynamics model, the nonlinear finite element model of a track-bridge structure under an earthquake, and the wheel-rail contact model are combined into an earthquake vehicle-bridge model based on structural nonlinear restoring force. Then, based on the earthquake vehicle-bridge model, a temporal evaluation network TAB integrating a time convolutional network TCN, a self-attention mechanism SA, and a bidirectional long short-term memory network BiLSTM is established to obtain a physical mapping relationship between seismic motion and nonlinear restoring force. Then, according to the physical mapping relationship between seismic motion and nonlinear restoring force, the nonlinear restoring force of the support structure is evaluated and the evaluation operation of the nonlinear restoring force of the bridge support structure is completed. This effectively realizes that the method and system for evaluating the nonlinear restoring force of the bridge support structure have the advantages of adopting a direct model of seismic motion input. The pseudo-support structural relationship can further simulate the support restoring force and quickly and accurately evaluate the nonlinear restoring force of the train-track-bridge. When the train model enters the bridge, positive transverse and vertical seismic waves are loaded until the train leaves the bridge, thereby obtaining the longitudinal-transverse restoring force of the supports at each position and the seismic-tectonic seismic-restoring force. At the same time, the time convolution network TCN can effectively capture multivariate time series information, and the self-attention mechanism SA solves the problem that the fully connected neural network cannot establish associations for multiple related inputs. The self-attention mechanism SA can simultaneously process the correlation between different parts of the entire sequence data, thereby achieving a high degree of parallelization of the calculation process, and then effectively capture the global contextual relationship and model the long-term dependency relationship. The effect is obvious. The bidirectional long short-term memory network BiLSTM can further optimize the model's processing ability for time series data and simultaneously consider the forward and backward information of the time series to improve the model evaluation accuracy.

[0147] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the foregoing embodiments. The foregoing embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for evaluating the nonlinear restoring force of bridge bearing structures based on hybrid deep learning, characterized by: The following steps are included: Step A: Construct a vehicle multi-rigid body dynamics model, a nonlinear finite element model of the track-bridge structure under earthquake conditions, and a wheel-rail contact model. Then, these models are combined into a seismic vehicle-bridge model based on structural nonlinear restoring force. The specific steps are as follows: Step A1: Construct a multi-rigid body dynamics model of the vehicle, where the motion equation of a single rigid body is expressed as shown in formula (1) and formula (2). Among them, m i is the mass of the i-th rigid body, I is the unit matrix, J i is the principal inertia tensor of the center of the i-th rigid body, F i and M i are the principal vector and principal moment of the suspension force and contact force related to the absolute coordinate system, ω i is the projection of the instantaneous angular velocity vector in the absolute coordinate system; Step A2: Construct a nonlinear finite element model of the track-bridge structure under earthquake conditions. The specific steps are as follows: Step A21: Based on Hamilton's principle, the motion equation of the track-bridge structure is established, as shown in formula (3): Among them, [M TB ]、[C TB ] and [K TB ] are the mass matrix, damping matrix and stiffness matrix of the track-bridge structure system, respectively. con } represents the equivalent nodal load vector of the contact between wheelset and rail, {F g } represents the vector of external additional loads such as earthquake load and gravity; Step A22, describe the material nonlinearity of the structure by macroscopic component internal force-deformation to establish a restoring force model, as shown in formula (4), Where x is the deformation of the component and g is the hysteretic restoring force; Step A23, decompose the hysteresis restoring force g into the sum of the elastic force and the hysteresis force, as shown in formula (5), Among them, αkx is the elastic force part, z is the hysteresis displacement; Step A24, solve the hysteresis displacement z, as shown in formula (6), Among them, ε() is the unit step function, x y is the yield displacement of the component; In step A25, a nonlinear finite element model of the track-bridge structure of key components is established using the local nonlinear force updating technology, thereby obtaining the corrected nonlinear track-bridge structure motion equation as shown in formula (7): Among them, {F K } and {F C } are load correction terms caused by structural stiffness and damping nonlinearity respectively; Step A26, set the earthquake acceleration to The motion equation of the track-bridge under earthquake is shown in formula (8): Step A3: constructing a wheel-rail contact model, wherein the wheel-rail contact model includes wheel-rail contact position search and wheel-rail contact force calculation. The specific steps are as follows: Step A31, searching for the wheel-rail contact position, wherein the wheel-rail contact is determined using the trace method; Step A32: Calculate the wheel-rail contact force, specifically by using a Hertz nonlinear spring to update the wheel-rail contact normal force, and then using Kalker theory to calculate the tangential creep force; Step B: Based on the earthquake vehicle-bridge model, a temporal evaluation network TAB is established that integrates the temporal convolutional network (TCN), the self-attention mechanism (SA), and the bidirectional long short-term memory (BiLSTM) network to obtain the physical mapping relationship between ground motion and nonlinear restoring force. Step C: Evaluate the nonlinear restoring force of the bearing structure based on the physical mapping relationship between earthquake motion and nonlinear restoring force, and complete the nonlinear restoring force evaluation operation of the bridge bearing structure.

2. The method for evaluating the nonlinear restoring force of a bridge support structure based on hybrid deep learning according to claim 1 is characterized by: Step B: Based on the earthquake bridge model, a temporal evaluation network TAB is established that integrates the temporal convolutional network TCN, the self-attention mechanism SA, and the bidirectional long short-term memory network BiLSTM to obtain the physical mapping relationship between earthquake motion and nonlinear restoring force. The specific steps are as follows: Step B1, constructing a temporal convolutional network (TCN), wherein the temporal convolutional network (TCN) is used to capture multivariate time series information, and the temporal convolutional network (TCN) is composed of dilated causal convolution (DCC); Step B2: establishing a self-attention mechanism SA, which is used to simultaneously process the correlation of different parts of the entire sequence data and make the calculation process highly parallel; Step B3, construct a bidirectional long short-term memory network BiLSTM, which is used to further optimize the model's processing ability for time series data and simultaneously consider the forward and backward information of the time series to improve the model evaluation accuracy. The bidirectional long short-term memory network BiLSTM specifically uses memory units to store long-term historical information, and then selectively retains and updates the information through a forget gate, an input gate, and an output gate. The forget gate is used to selectively discard long-term memory, the input gate is used to update long-term memory, and the output gate is used to combine short-term memory and long-term memory to output the current moment result.

3. The method for evaluating the nonlinear restoring force of a bridge support structure based on hybrid deep learning according to claim 1 is characterized by: Step C: evaluate the nonlinear restoring force of the support structure according to the physical mapping relationship between earthquake motion and nonlinear restoring force, and complete the evaluation of the nonlinear restoring force of the bridge support structure. Specifically, the mean absolute error (MAE), root mean square error (RMSE) and determination coefficient (R) are used to calculate the nonlinear restoring force of the support structure. 2 The nonlinear restoring force of the support structure is evaluated, as shown in formula (19), Where Ω is the sample size, Y j is the evaluation value, T j is the true value, is the true mean value.

4. A bridge support structure nonlinear restoring force evaluation system based on hybrid deep learning, wherein the specific evaluation process of the bridge support structure nonlinear restoring force evaluation system is based on the bridge support structure nonlinear restoring force evaluation method according to any one of claims 1 to 3, characterized in that: The system includes an earthquake vehicle-bridge model construction module, a restoring force physical mapping relationship acquisition module, and a support structure nonlinear restoring force evaluation module. The earthquake vehicle-bridge model construction module is used to construct a vehicle multi-rigid body dynamics model, a nonlinear finite element model of the track-bridge structure under earthquake conditions, and a wheel-rail contact model. The vehicle multi-rigid body dynamics model, the nonlinear finite element model of the track-bridge structure under earthquake conditions, and the wheel-rail contact model are then combined into an earthquake vehicle-bridge model based on structural nonlinear restoring force. The restoring force physical mapping relationship acquisition module is used to establish a temporal evaluation network TAB that integrates a time convolutional network TCN, a self-attention mechanism SA, and a bidirectional long short-term memory network BiLSTM based on an earthquake vehicle-bridge model and obtain a physical mapping relationship between earthquake motion and nonlinear restoring force; The support structure nonlinear restoring force evaluation module is used to evaluate the nonlinear restoring force of the support structure according to the physical mapping relationship between earthquake motion and nonlinear restoring force and complete the nonlinear restoring force evaluation operation of the bridge support structure.

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