Bridge support structure nonlinear restoring force evaluation method and system based on hybrid deep learning

Abstract

The invention discloses a bridge support structure nonlinear restoring force evaluation method and system based on hybrid deep learning, and the method comprises the steps: firstly constructing a vehicle multi-rigid-body dynamic model, a rail-bridge structure nonlinear finite element model under an earthquake, and a wheel-rail contact model; combining the vehicle multi-rigid-body dynamic model, the nonlinear finite element model of the rail-bridge structure under the earthquake and the wheel-rail contact model into an earthquake axle model based on the nonlinear restoring force of the structure; according to the invention, seismic oscillation input is adopted to directly simulate the structural relationship of the support so as to further simulate the restoring force of the support and rapidly and accurately evaluate the nonlinear restoring force of the train-rail-bridge; and when the train model enters the bridge, positive transverse and vertical seismic waves are loaded until the train leaves the bridge, so that the longitudinal-transverse restoring force of the support at each position and the seismic-restoring force of the seismic oscillation structure are obtained, and the method is suitable for being widely popularized and used.

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 the bridge bearing structure refers to the nonlinear mechanical characteristics of the bearing during its deformation and recovery process after being subjected to external forces. The bridge bearing is an important component connecting the bridge superstructure and the substructure, and it is responsible for reliably transmitting the reaction force and deformation of the bridge superstructure to the substructure. However, under extreme working conditions such as earthquakes, the force situation of the bearing becomes complicated, and its restoring force no longer presents a simple linear relationship, but rather exhibits nonlinearity.

[0003] At present, under the action of earthquakes, most track-bridge structures will enter different degrees of plastic damage. In addition, due to the large overall stiffness of the high-speed railway track-bridge structure, the main nonlinear form of the high-speed railway track-bridge structure is the elastic-plasticity of the material, and it is less likely to cause structural failure caused by geometric nonlinearity. The evaluation process of the existing bridge support structure nonlinear restoring force evaluation method generally has low computational efficiency, resulting in a large amount of evaluation time being consumed during the evaluation process. Not only is the evaluation result low in accuracy and reliability, but there is also a serious safety hazard of misjudgment of 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 bearing structure nonlinear restoring force evaluation method is generally low in computational efficiency, which results in a large amount of evaluation time being consumed in the evaluation process. Not only is the evaluation result low in accuracy and reliability, but there is also a safety hazard of misjudgment of serious bridge damage. A bridge bearing structure nonlinear restoring force evaluation method and system based on hybrid deep learning is provided, which realizes the function of directly simulating the bearing structure relationship by using seismic input to further simulate the bearing restoring force and quickly and accurately perform nonlinear restoring force evaluation on 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-lateral restoring force of the bearing 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 bearing structure based on hybrid deep learning, comprising the following steps:

[0007] Step A, constructing a vehicle multi-rigid body dynamics model, a nonlinear finite element model of the track-bridge structure under earthquake, and a wheel-rail contact model, and then combining the vehicle multi-rigid body dynamics model, the nonlinear finite element model of the track-bridge structure under earthquake, and the wheel-rail contact model into an earthquake vehicle-bridge model based on structural nonlinear restoring force;

[0008] 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 the earthquake motion and the nonlinear restoring force;

[0009] Step C, evaluating the nonlinear restoring force of the bearing structure according to the physical mapping relationship between earthquake motion and nonlinear restoring force, and completing the evaluation operation of the nonlinear restoring force of the bridge bearing structure.

[0010] The aforementioned method for evaluating the nonlinear restoring force of a bridge support structure based on hybrid deep learning, step A, constructing a vehicle multi-rigid body dynamics model, a nonlinear finite element model of a track-bridge structure under earthquake, and a wheel-rail contact model, and then combining the vehicle multi-rigid body dynamics model, the nonlinear finite element model of a track-bridge structure under earthquake, and the wheel-rail contact model 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, constructing a nonlinear finite element model of the track-bridge structure under earthquake. The specific steps are as follows:

[0015] Step A21, establish the motion equation of the track-bridge structure based on Hamilton's principle, 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 node 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, describing the material nonlinearity of the structure through macroscopic component internal force-deformation to establish a restoring force model, as shown in formula (4),

[0019]

[0020] Among them, x is the deformation of the component, and g is the hysteretic restoring force;

[0021] Step A23, decomposing 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 component yield displacement;

[0027] Step A25, using the local nonlinear force updating technology to establish the nonlinear finite element model of the track-bridge structure of the key components, 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 the load correction terms caused by structural stiffness and damping nonlinearity respectively;

[0030] Step A26, setting the earthquake acceleration to Then 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 by using a 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 nonlinear restoring force evaluation method of bridge bearing structure based on hybrid deep learning, step B, based on the earthquake vehicle-bridge model, establishes a temporal evaluation network TAB integrating 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 a dilated causal convolution DCC;

[0037] Step B2, establishing a self-attention mechanism SA, wherein the self-attention mechanism SA 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, 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 information 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, wherein 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 bearing structure based on hybrid deep learning, step B1 has the following specific steps:

[0040] Step B11, construct a 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] Among them, 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, the causal expansion convolution residual module 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, and if the input dimension and output dimension are different, a 1×1 convolution is used as the cross-path layer to ensure the dimensional matching of the feature matrix.

[0047] The aforementioned method for evaluating the nonlinear restoring force of a bridge bearing structure based on hybrid deep learning, the specific steps of step B2 are as follows:

[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 positions. 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, the attention is calculated in parallel on each block. After the calculation, the attention results of each block are concatenated and combined through linear transformation. The independent scaled dot product attention calculations are synthesized 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 bearing structure based on hybrid deep learning, step B3 has the following specific 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] Among them, σ is the sigmoid activation function, tanh is the hyperbolic tangent activation function, ⊙ is the point multiplication 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 so as to mine the forward and backward dependencies of the time series, reverse LSTM B and forward LSTM F As shown in formulas (15) and (16),

[0062]

[0063] The arrow is 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 integrating the temporal convolutional network TCN, the self-attention mechanism SA and the bidirectional long short-term memory network BiLSTM. The temporal evaluation network TAB adopts 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 bearing structure based on hybrid deep learning, step C, evaluates the nonlinear restoring force of the bearing structure according to the physical mapping relationship between ground motion and nonlinear restoring force, and completes the evaluation of the nonlinear restoring force of the bridge bearing structure, specifically using the mean absolute error MAE, calculating the root mean square error RMSE and the determination coefficient R 2 The nonlinear restoring force of the support structure is evaluated, as shown in formula (19):

[0071]

[0072] Among them, 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 a bridge bearing structure based on hybrid deep learning comprises an earthquake vehicle-bridge model construction module, a restoring force physical mapping relationship acquisition module and a bearing structure nonlinear restoring force evaluation module, wherein 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 earthquake and a wheel-rail contact model, and then the vehicle multi-rigid body dynamics model, the track-bridge structure nonlinear finite element model under earthquake and the wheel-rail contact model are 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 integrating a temporal 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 bearing structure nonlinear restoring force evaluation module is used to evaluate the nonlinear restoring force of the bearing structure according to the seismic motion-nonlinear restoring force physical mapping relationship and complete the bridge bearing 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 bearing 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 integrating a time convolution 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 seismic motion and nonlinear restoring force, and then evaluates the nonlinear restoring force of the bearing structure according to the physical mapping relationship between seismic motion and nonlinear restoring force and completes the evaluation operation of the nonlinear restoring force of the bridge bearing structure; the nonlinear restoring force evaluation method and system of the bridge bearing structure have the advantages of adopting a direct seismic input 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, the positive transverse and vertical seismic waves are loaded until the train leaves the bridge, so as to obtain the longitudinal-lateral 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 realizing 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. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0076] Figure 2 It is a comparison diagram 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 in conjunction with the accompanying drawings.

[0078] like Figure 1 As shown, a method and system for evaluating the nonlinear restoring force of a bridge bearing structure based on hybrid deep learning of the present invention comprises 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, and a wheel-rail contact model, and then combine the vehicle multi-rigid body dynamics model, the nonlinear finite element model of the track-bridge structure under earthquake, and the wheel-rail contact model into an earthquake 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, constructing a nonlinear finite element model of the track-bridge structure under earthquake. The specific steps are as follows:

[0085] Step A21, establish the motion equation of the track-bridge structure based on Hamilton's principle, 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 node 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, describing the material nonlinearity of the structure through macroscopic component internal force-deformation to establish a restoring force model, as shown in formula (4),

[0089]

[0090] Among them, x is the deformation of the component, and g is the hysteretic restoring force;

[0091] Step A23, decomposing 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] Step A25, using the local nonlinear force updating technology to establish the nonlinear finite element model of the track-bridge structure of the key components, 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 the load correction terms caused by structural stiffness and damping nonlinearity respectively;

[0100] Step A26, setting the earthquake acceleration to Then 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 by using a 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, 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 to obtain the physical mapping relationship between the earthquake motion and the nonlinear restoring force. The specific steps are as follows:

[0106] 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. The specific steps are as follows:

[0107] Step B11, construct a 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] Among them, 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, constructing a causal expansion convolution residual module, the causal expansion convolution residual module 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, and then the output features of the previous layer are 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, and if the input dimension and the output dimension are different, a 1×1 convolution is used as a cross-path layer to ensure the 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 positions. 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, the attention is calculated in parallel on each block. After the calculation, the attention results of each block are concatenated and combined through linear transformation. The independent scaled dot product attention calculations are synthesized 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, 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 information 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, wherein 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] Among them, σ is the sigmoid activation function, tanh is the hyperbolic tangent activation function, ⊙ is the point multiplication 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 so as to mine the forward and backward dependencies of the time series, reverse LSTM B and forward LSTM F As shown in formulas (15) and (16),

[0129]

[0130] The arrow is 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 integrating the temporal convolutional network TCN, the self-attention mechanism SA and the bidirectional long short-term memory network BiLSTM. The temporal evaluation network TAB adopts 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 bearing 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 bearing 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 bearing structure. 2 The nonlinear restoring force of the support structure is evaluated, as shown in formula (19):

[0138]

[0139] Among them, 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 a bridge bearing structure based on hybrid deep learning comprises an earthquake vehicle-bridge model construction module, a restoring force physical mapping relationship acquisition module and a bearing structure nonlinear restoring force evaluation module, wherein 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 earthquake and a wheel-rail contact model, and then the vehicle multi-rigid body dynamics model, the track-bridge structure nonlinear finite element model under earthquake and the wheel-rail contact model are 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 integrating a temporal 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 bearing structure nonlinear restoring force evaluation module is used to evaluate the nonlinear restoring force of the bearing structure according to the seismic motion-nonlinear restoring force physical mapping relationship and complete the bridge bearing structure nonlinear restoring force evaluation operation.

[0141] In order to better illustrate the use effect of the present invention, a specific embodiment of the present invention is introduced below. The overall data set of this embodiment is divided into 60% training, 20% verification and 20% test sets. The data will be randomly shuffled before training to ensure fair comparison of the evaluation results. The network of this embodiment is implemented using the matlab platform, and the training of the evaluation model is carried out on the NVIDIA GTX3090 GPU. The model of this embodiment is trained for 200 epochs, the batch size of the network is set to 128, and the Adam optimizer with an initial learning rate of 0.01 is used. In order to enhance convergence, the learning rate gradient decreases, and the decrease rate is 25% for 10 epochs; the weight initialization is set to the standard Gaussian distribution, the basic filterSize is set to 3, numFilters is set to 128, and the dropoutFactor is set to 0.2. The data is shuffled in each epoch, and the network is verified once every 10 epochs. This embodiment uses an early stopping strategy and sets L2 regularization to prevent overfitting. The early stopping is set to stop the model training after 20 epochs when the accuracy is not significantly improved, and the L2 regularization value is set to 0.001.

[0142] like Figure 2 The figure shows the prediction accuracy and PSD comparison of the nonlinear restoring force of the bearing under different seismic 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 bearing, and has significant prediction accuracy in both time domain and frequency domain. At the same time, there is little difference in the evaluation accuracy under different earthquakes. The present invention has significant advantages in evaluation stability.

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

[0144]

[0145] As shown in Table 1, the evaluation results of the accuracy of different span supports are shown in Table 1. As can be seen from Table 1, the TAB network proposed in the present invention shows excellent performance in different span fixed supports and sliding supports. R2 is greater than 90%, among which the R2 of span 1 sliding support and span 3 fixed support exceeds 99%, which can prove that the network has significant advantages in data interpretation ability, fitting ability, model accuracy and reliability.

[0146] In summary, the present invention provides a method and system for evaluating the nonlinear restoring force of a bridge bearing 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 bearing structure is evaluated and the evaluation operation of the nonlinear restoring force of the bridge bearing structure is completed. This effectively realizes that the method and system for evaluating the nonlinear restoring force of the bridge bearing structure have the advantages of adopting a direct modeling method using 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, the positive transverse and vertical seismic waves are loaded until the train leaves the bridge, thereby obtaining the longitudinal-lateral 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 correlations 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 above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A method for evaluating the nonlinear restoring force of a bridge bearing structure based on hybrid deep learning, characterized in that: The following steps are included: Step A, constructing a vehicle multi-rigid body dynamics model, a nonlinear finite element model of the track-bridge structure under earthquake, and a wheel-rail contact model, and then combining the vehicle multi-rigid body dynamics model, the nonlinear finite element model of the track-bridge structure under earthquake, and the wheel-rail contact model into an earthquake vehicle-bridge model based on structural nonlinear restoring force; 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 the earthquake motion and the nonlinear restoring force; Step C, evaluating the nonlinear restoring force of the bearing structure according to the physical mapping relationship between earthquake motion and nonlinear restoring force, and completing the evaluation operation of the nonlinear restoring force of the bridge bearing structure.

2. According to claim 1, a method for evaluating the nonlinear restoring force of a bridge bearing structure based on hybrid deep learning is characterized in that: Step A, construct a vehicle multi-rigid body dynamics model, a nonlinear finite element model of the track-bridge structure under earthquake, and a wheel-rail contact model, and then combine the vehicle multi-rigid body dynamics model, the nonlinear finite element model of the track-bridge structure under earthquake, and the wheel-rail contact model into an earthquake 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, constructing a nonlinear finite element model of the track-bridge structure under earthquake. The specific steps are as follows: Step A21, establish the motion equation of the track-bridge structure based on Hamilton's principle, 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 node 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, describing the material nonlinearity of the structure through macroscopic component internal force-deformation to establish a restoring force model, as shown in formula (4), Among them, x is the deformation of the component, and g is the hysteretic restoring force; Step A23, decomposing 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 component yield displacement; Step A25, using the local nonlinear force updating technology to establish the nonlinear finite element model of the track-bridge structure of the key components, thereby obtaining the corrected nonlinear track-bridge structure motion equation as shown in formula (7), Among them, {F K } and {F C } are the load correction terms caused by structural stiffness and damping nonlinearity respectively; Step A26, set the earthquake acceleration to {ü b }, then the motion equation of the track-bridge under earthquake is as 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 by using a trace method; 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.

3. The method for evaluating the nonlinear restoring force of a bridge bearing structure based on hybrid deep learning according to claim 2 is characterized in that: Step B, based on the earthquake bridge model, 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 to obtain the physical mapping relationship between the earthquake motion and the 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 a dilated causal convolution DCC; Step B2, establishing a self-attention mechanism SA, wherein the self-attention mechanism SA 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, 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 information 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, wherein 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.

4. The method for evaluating the nonlinear restoring force of a bridge bearing structure based on hybrid deep learning according to claim 3 is characterized in that: Step B1 The specific steps are as follows: Step B11, construct a 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), Among them, k is the size of the filter, w(j) is the weight of the convolution kernel, and * is the convolution operation; Step B12, adjust the expansion factor to expand the receptive field R of the temporal convolutional network TCN field , as shown in formula (10), R field =K·(N stack -1)·d i +1 (10) Among them, d i is the expansion factor; Step B13, construct a causal expansion convolution residual module, the causal expansion convolution residual module 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, and if the input dimension and output dimension are different, a 1×1 convolution is used as the cross-path layer to ensure the dimensional matching of the feature matrix.

5. The method for evaluating the nonlinear restoring force of a bridge bearing structure based on hybrid deep learning according to claim 4 is characterized in that: The specific steps of step B2 are as follows: Step B21, for input feature X = {x1, x2, ..., x T } is matrixed, as shown in formula (11), in, To optimize the scaling factor of training, Q is Query, and K is the Key, and V is Value, and Step B22, expands the attention to local features at multiple positions. 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, the attention is calculated in parallel on each block. After the calculation, the attention results of each block are concatenated and combined through linear transformation. The independent scaled dot product attention calculations are synthesized by linear transformation to obtain the final output value, as shown in formulas (12) and (13). MultiHead(Q,K,V)=COncatenate(head1,…,head h )W o (12) head i =Attention(QW i Q ,KW i K ,VW i V ) (13) in, and are all self-attention weights, is the multi-head attention weight, and Concatenate is the concatenation operation.

6. The method for evaluating the nonlinear restoring force of a bridge bearing structure based on hybrid deep learning according to claim 5 is characterized in that: Step B3: The specific steps are as follows: 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), Among them, σ is the sigmoid activation function, tanh is the hyperbolic tangent activation function, ⊙ is the point multiplication operation; W and b are the weights and biases of various gates respectively; Step B32, add time flow data information from the future to the past so as to mine the forward and backward dependencies of the time series, reverse LSTM B and forward LSTM F As shown in formulas (15) and (16), The arrow is 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, 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), in, To sum by weight; Step B4, establish a temporal evaluation network TAB integrating the temporal convolutional network TCN, the self-attention mechanism SA and the bidirectional long short-term memory network BiLSTM. The temporal evaluation network TAB adopts Huber Loss as the loss function, as shown in formula (18), 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.

7. The method for evaluating the nonlinear restoring force of a bridge bearing structure based on hybrid deep learning according to claim 6 is characterized in that: Step C, evaluate the nonlinear restoring force of the bearing structure according to the physical mapping relationship between seismic motion and nonlinear restoring force, and complete the evaluation of the nonlinear restoring force of the bridge bearing 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 bearing structure. 2 The nonlinear restoring force of the support structure is evaluated, as shown in formula (19): Among them, Ω is the sample size, Y j is the evaluation value, T j is the true value, is the true mean value.

8. 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 7, characterized in that: It 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 earthquake, and a wheel-rail contact model, and then the vehicle multi-rigid body dynamics model, the track-bridge structure nonlinear finite element model under earthquake, and the wheel-rail contact model are combined 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 time series evaluation network TAB integrating a time convolution 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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