High-speed rail system sliding layer peak displacement envelope curve and rail direction irregularity prediction method considering seismic oscillation and pier height uncertainty and application

Abstract

The invention discloses a high-speed rail system sliding layer peak displacement envelope curve and rail direction irregularity prediction method considering seismic oscillation and pier height uncertainty and application. The method comprises the following steps: constructing a multi-mode hybrid neural network model TransTCN embedded with field priori knowledge; feature extraction is carried out on multi-modal input features of a time sequence based on seismic oscillation fusion structure features and a space sequence for outputting peak displacement based on an elastic response spectrum method; the pier height features and the seismic oscillation features are subjected to dimension fusion to serve as time sequence features, and a time dependency relationship is processed; processing a spatial dependency relationship by taking an elastic response spectrum analysis result as a spatial feature; and jointly inputting the extracted features into a constructed multi-mode hybrid neural network model TransTCN, and realizing prediction of the peak displacement envelope curve and rail direction irregularity of the sliding layer of the high-speed rail system under the consideration of seismic oscillation and pier height uncertainty. The prediction precision is improved, the training sample demand is reduced, the regional high-speed rail system damage is rapidly evaluated, and the practical value is good.

Description

Technical Field

[0001] The present invention relates to a method and application for predicting a peak displacement envelope curve of a sliding layer of a high-speed railway system and track irregularity taking into account the uncertainty of earthquake motion and pier height. Background Art

[0002] As China's high-speed railway network construction extends to earthquake-prone areas, the complexity of the track-bridge system makes it more vulnerable to damage under earthquakes, endangering the structure and driving safety. Therefore, improving the high-speed rail line's ability to cope with major natural disasters and ensure traffic capacity is a research focus. When the existing high-speed rail network is affected by an earthquake, in order to ensure driving safety, the general measure of directly interrupting train operation is adopted. The inherent resilience of the track-bridge system is not effectively considered. The strategy is too conservative, which seriously hinders the progress of post-disaster rescue. Therefore, quickly assessing and repairing the structural damage and track deformation caused by multiple track-bridge systems as much as possible within a limited time can effectively guide post-earthquake disaster relief and ensure driving safety.

[0003] The traditional post-earthquake safety prediction and assessment method of track-bridge system is to evaluate the degree of earthquake damage by calculating the node response of key components and to evaluate driving safety by using track surface deformation to calculate track irregularity. However, the data used in these assessment methods are all derived from physics-based alternative models, that is, obtained through nonlinear finite element time-history analysis. Due to the randomness of earthquake excitation and changes in structural characteristics, when the design or assessment is extended to multiple structures, the efficiency of performing time-history analysis on each model is low, so the computational cost of developing complex numerical models and performing analysis limits their actual adoption.

[0004] In addition, existing evaluation methods mostly use the response spectrum method (RSM) to estimate the average peak response of the multi-degree-of-freedom (MDOF) system. Although this method has good response prediction accuracy in practical applications, the RSM method cannot effectively deal with the nonlinearity of the structure, and as the predicted structural degrees of freedom (DOFs) increase, the prediction error increases significantly, which will seriously threaten the correct evaluation of structural damage and driving safety.

[0005] There are also reports that use deep learning-based methods to use data-driven models to achieve nonlinear mapping of dynamic responses and improve computational efficiency. However, these methods are all neural network response prediction frameworks used in the field of buildings, and usually focus on the response prediction of a single key position or a single node, and evaluate the overall damage degree of the building through the response of the inter-story displacement angle or the key beam column. When the structure is a longitudinally long structure such as a road, bridge, or high-speed railway, a single target prediction is difficult to reflect the overall earthquake damage of the structure, and the prediction target is naturally transferred to the peak displacement envelope of the long-line structure or various overall linear indicators. At the same time, the stiffness of the bridge pier will significantly affect the upper structure response of the track-bridge system, and the damage will be mapped to the deformation of the track surface. The deformation and damage of the track structure after the earthquake will significantly affect the safety of train driving after the earthquake; therefore, considering the uncertainty of the pier height, the overall response to the earthquake damage of the high-speed railway network is used to timely evaluate the driving risk. In addition, a large number of training samples are essential to achieve accurate response prediction for structures with complex degrees of freedom and high nonlinearity. Therefore, how to reduce the training requirements and achieve high-precision response prediction with a smaller sample size is also an important challenge.

[0006] Therefore, how to fully consider the inherent resilience of the track-bridge system, evaluate the degree of damage to the track-bridge system and the deformation of the track surface as quickly as possible under the uncertainty of ground motion and pier height, overcome the computational burden of purely physics-based proxy models and the modeling difficulties caused by changes in structural parameters, and at the same time significantly improve the fitting accuracy of pure data-driven models and reduce the demand for training data, are still urgent issues to be solved. Summary of the invention

[0007] In order to solve the above problems and to achieve the above objectives, the present invention first provides a method for predicting the peak displacement envelope curve of the sliding layer of a high-speed railway system and track irregularity considering the uncertainty of ground motion and pier height, which specifically includes the following steps:

[0008] 1) Construct a multimodal hybrid neural network model TransTCN that embeds domain prior knowledge;

[0009] 2) Multimodal input feature extraction is performed on the time series based on the fusion of the pier height feature based on the earthquake motion feature and the spatial series based on the output peak displacement of the elastic response spectrum method; the earthquake motion feature and the pier height feature are used as the time series feature through dimensional fusion to deal with the time dependency; the elastic response spectrum method analysis results are used as the spatial feature to deal with the spatial dependency;

[0010] 3) The multimodal input features extracted in step 2) are input into the multimodal hybrid neural network model TransTCN constructed in step 1) for processing, so as to realize the prediction of the peak displacement envelope curve and track irregularity of the high-speed railway system sliding layer considering the uncertainty of ground motion and pier height.

[0011] In the above-mentioned method for predicting the peak displacement envelope curve of the sliding layer and track irregularity of the high-speed railway system considering the uncertainty of ground motion and pier height, in step 1), the multimodal hybrid neural network model TransTCN is a long sequence prediction framework combining Transformer and TCN networks, which includes a Transformer module and a TCN module;

[0012] The Transformer module is used to capture the temporal characteristics of earthquake motion and the spatial structure characteristics of the response spectrum method, and includes an embedding layer, a multi-head self-attention layer, and a fully connected feedforward network layer;

[0013] The TCN module is used to capture the complete temporal dependencies, which includes multiple dilated causal convolutional layers and a cross-path layer, and uses rectified linear units as activation functions and batch normalization as convolution filters.

[0014] In the above-mentioned method for predicting the peak displacement envelope curve of the sliding layer of the high-speed railway system and the track irregularity considering the uncertainty of the earthquake motion and the pier height, in step 2), the time series based on the earthquake motion fusion structural characteristics is a sequence obtained by the fusion of seismic data processing and pier height characteristics, and the specific fusion process is as follows:

[0015] The earthquake motion sequence is expressed as E = {e1, e2, …, e t}∈R t , where e t is the seismic acceleration at each moment, and t is the time sequence number;

[0016] The pier height sequence is expressed as P = {p1, p2, ..., p s-1}∈R s-1 , p s-1 is the height of the bridge pier, s is the number of bridge spans;

[0017] The predicted output of the post-seismic peak displacement envelope or track irregularity of the structure is O = {O1, O2, …, Oα}∈Rα, where O k is the peak displacement of the output point, α is the number of nodes at the predicted location of the structure;

[0018] Using multiplication fusion, the structural characteristic time series of a single fused ground motion is expressed as:

[0019] PE in =P T E (1);

[0020] Where: P is the pier height sequence; E is the earthquake motion sequence; PE in represents input features; T represents transposition operation.

[0021] In the above-mentioned high-speed railway system sliding layer peak displacement envelope curve and track irregularity prediction method considering the uncertainty of ground motion and pier height, in step 2), the spatial sequence of peak displacement output based on elastic response spectrum method is the analysis result of integrating domain prior knowledge into neural network by using response spectrum method. The specific analysis process is as follows:

[0022] For a multi-span high-speed railway track bridge system composed of any structure, its motion equation is expressed as A spring-mass system with damping in degrees of freedom:

[0023]

[0024] Where:

[0025] M is the mass matrix of the multi-span high-speed railway track bridge system;

[0026] C is the damping matrix of the multi-span high-speed railway track bridge system;

[0027] K is the stiffness matrix of the multi-span high-speed railway track bridge system;

[0028] is the acceleration vector of the multi-span high-speed railway track bridge system;

[0029] is the velocity vector of the multi-span high-speed railway track bridge system;

[0030] x(t) is the displacement vector of the multi-span high-speed railway track bridge system;

[0031] P(t) is the equivalent load acting on the system;

[0032] Among them, C is the classic Rayleigh damping, and the equation can be naturally decoupled;

[0033] Under a given earthquake motion sequence, P(t) can be expressed as:

[0034]

[0035] Where: ι represents the influence vector, represents ground acceleration;

[0036] For a linear elastic system with multiple degrees of freedom, the system response is expressed as an effective combination of multiple modal components:

[0037]

[0038] Where:

[0039] u(t) is the total response of the system;

[0040] u n(t) is the nth-order modal response;

[0041] is the static response of the nth mode;

[0042] A n (t) is the pseudo-acceleration response of the nth mode,

[0043] N is the number of modes,

[0044] n represents the modal order;

[0045] Among them A n (t) is:

[0046]

[0047] Where:

[0048] A n (t) is the pseudo-acceleration response of the nth mode;

[0049] represents the square of the natural frequency of the nth mode;

[0050] D n (t) is the displacement response of the system;

[0051] The static response of the nth modal for

[0052]

[0053] Where:

[0054] Γ n represents the modal participation factor,

[0055] φ n The nth order mode shape vector;

[0056] Since the modal static response is related to the modal participation factor, modal frequency and modal vibration shape vector;

[0057] Combining equations (4)-(6), the system total response u(t) equation is transformed into:

[0058]

[0059] Where Γ n and φ n represent the modal participation factor and the nth-order mode shape vector respectively;

[0060] Obtaining the maximum structural response during the earthquake excitation period is a key step in the seismic design or seismic assessment of the structure, that is, solving,

[0061]

[0062] Where:

[0063] u no =Γ n φ n D n (t),

[0064] represents the peak response of the nth mode, obtained by response spectrum calculation;

[0065] The correlation between the peak modal responses is taken into account to prevent significant errors, and the perfect square combination method is used to predict the maximum response of the structure when the modal responses have significant cross-correlation:

[0066]

[0067] In the formula, ρ in represents the correlation between the i-th and n-th modal responses; the formula can be expanded as:

[0068]

[0069] In the CQC rule, the modal correlation coefficient ρ in Calculated by the following formula:

[0070]

[0071] Where:

[0072] u o is the maximum response of the structure,

[0073] N is the number of modes,

[0074] u io is the peak response of the ith mode,

[0075] ζ i is the damping ratio of the i-th mode, which indicates the ability of this mode to dissipate vibration energy.

[0076] ζ n is the damping ratio of the nth mode,

[0077] represents the natural frequency ratio of the i-th mode to the n-th mode,

[0078] ω i and ω n are the natural frequencies of the i-th mode and the n-th mode respectively.

[0079] In the above-mentioned method for predicting the peak displacement envelope curve of the sliding layer of the high-speed railway system and the track irregularity considering the uncertainty of the earthquake motion and the pier height, in step 3), the features extracted in step 2) are input into the multimodal hybrid neural network model TransTCN constructed in step 1), and the specific processing is as follows:

[0080] After the time series of structural characteristics based on earthquake motion fusion and the spatial series of peak displacement output based on elastic response spectrum method are input into the multimodal hybrid neural network model TransTCN, they first pass through the embedding layer of the Transformer module to encode the position of the input sequence and convert it into a vector sequence, and then process it through the multi-head self-attention layer to obtain the attention score of each sequence point and output the attention tensor of the current sequence position;

[0081] Then, the complete temporal dependency is captured through the TCN module, that is, the attention tensor obtained by the Transformer module is normalized and filtered, and the output features are enriched with temporal information through multiple dilated causal convolutional layers, using rectified linear units as activation functions, and further extracting tensor features of corresponding sequence positions through normalization as convolutional filters;

[0082] Huber Loss is used as the loss function, and the effective combination of mean square error and mean absolute error is achieved by fine-tuning the parameter δ. The output result is adjusted, and the adjusted network can be used to realize the prediction of the peak displacement envelope curve of the sliding layer and track irregularity of the high-speed railway system considering the uncertainty of ground motion and pier height.

[0083] As a preferred technical solution, the above-mentioned high-speed railway system sliding layer peak displacement envelope curve and track irregularity prediction method considering the uncertainty of ground motion and pier height,

[0084] The processing process of inputting the time series of structural characteristics based on ground motion fusion and the spatial series of peak displacement output based on elastic response spectrum method into the Transformer module is as follows:

[0085] Input TransTCN model features XS = {xs1, xs2, ..., xs t} is converted into three trainable linear mapping feature matrices by the embedding layer, named as: query key Sum

[0086] Among them, xs t is the characteristic of time series t, n model ,m model are the number of queries and the length of the input sequence in the attention module, respectively. k and d vare the feature dimensions of the query, key, and value matrices, respectively;

[0087] The scaled dot product attention and softmax function are used to consider its bidirectional temporal dependency on the historical sequence. The self-attention matrix is ​​expressed as

[0088]

[0089] in, It is the scaling factor for optimizing training to adjust the calculation of the inner product to prevent the inner product from being too large. In self-attention, d k and d v Equal; T is the transposition symbol;

[0090] Multiple queries key Sum Perform different linear transformation projections, and then calculate the attention on each segment in parallel. Combine h independent scaled dot product attention results through vector concatenation and linear transformation and obtain the output value through linear transformation, satisfying:

[0091] MultiHead(Q,K,V)=Concatenate(head1,…,head h )W o (14);

[0092] Where:

[0093] h represents the number of heads,

[0094] represents the multi-head attention weight,

[0095] head h represents the attention head,

[0096] Concatenate represents the concatenation operation;

[0097] For the hi-th attention head, a single attention is calculated through different weight matrices:

[0098]

[0099] Where: represents the self-attention weight, represents the multi-head attention weight, Attention is the self-attention calculation, d model It is the characteristic dimension of the entire model.

[0100] As a preferred technical solution, the aforementioned high-speed railway system sliding layer peak displacement envelope curve and track irregularity prediction method considering the uncertainty of ground motion and pier height, the complete time dependency capture process through the TCN module is:

[0101] One-dimensional time series input With filters f:{1,2,…,ζ-1}, the dilated convolution operation F on the elements θ in the one-dimensional sequence can be expressed as:

[0102]

[0103] Where:

[0104] θ represents the time step to be processed; ci is the time step currently being processed; cd is the dilation factor used to control the size of the interval; ζ is the size of the filter; * represents the convolution operation; It is a one-dimensional time series input;

[0105] The receptive field of TCN can be calculated as:

[0106]

[0107] Where: R field is the receptive field of TCN; N stack is the number of stacked TCN layers, that is, the number of stacked convolutional layers; is the size of the convolution kernel, cd is the expansion factor of each convolution layer;

[0108] The multimodal hybrid neural network model TransTCN adopts a residual module to avoid model degradation. The calculation process of the residual block is as follows:

[0109]

[0110] Where: Represents the feature representation learned by the DCC layer; It is the input and the output features obtained after the convolution operation of the DCC layer. These features can effectively represent the temporal information of the input sequence.

[0111] As a preferred technical solution, the aforementioned high-speed railway system sliding layer peak displacement envelope curve and track irregularity prediction method considering the uncertainty of ground motion and pier height, the multimodal hybrid neural network model TransTCN output layer uses Huber Loss as the loss function, which is defined as a piecewise function:

[0112]

[0113] Where: is the predicted value, is the true value, δ is the adjustment coefficient, which determines the transition threshold of the loss function from quadratic to linear;

[0114] By continuously adjusting δ to make the predicted output consistent with the actual output, the adjusted network can be used to realize the prediction of the peak displacement envelope curve of the sliding layer and track irregularity of the high-speed railway system considering the uncertainty of ground motion and pier height.

[0115] The above-mentioned method for predicting the peak displacement envelope curve of the sliding layer of the high-speed railway system and the track irregularity considering the uncertainty of the earthquake motion and the pier height, the method also includes the step of training the multi-modal hybrid neural network model TransTCN constructed in step 1), and the process of sampling the earthquake motion records and uncertainty parameters used in the training is:

[0116] The seismic records used for training, verification and testing are matched with the design response spectra that fully consider the seismic propagation path, site conditions, spectral characteristics and soil shear wave velocity, and then the training data sample library is obtained based on the Latin hypercube stratified sampling method;

[0117] The uncertainty parameter of the earthquake motion is E = [e1, e2] T and the uncertain parameters of pier height PH=[P1,P2,…,P S-1 ] T Construct S+1 dimensional probability space R U , represents the total space of uncertainties of all random variables including ground motion and pier height parameters;

[0118] Let ξ = s + 1, which represents the probability space dimension of the combination of bridge structure and ground motion;

[0119] For a ξ-dimensional random variable The random variables include all the pier height parameters and ground motion parameters, which together define R u Each sample point in ;

[0120] Decompose it into P mutually disjoint orthogonal subspaces where a single subspace ξ j The dimensions satisfy:

[0121]

[0122] It means that the sum of the dimensions of each subspace is equal to the dimension ξ of the entire probability space, and the dimension of each subspace does not exceed ξ;

[0123] At the same time, the orthogonality condition should be met:

[0124]

[0125] Where: is an empty set, ∩ and are the intersection operation and the union operation of all subspaces, respectively. Equations (21) and (22) indicate that different subspaces are independent of each other, that is, there is no overlap between them, and the union of all subspaces is equal to the original probability space R U ;

[0126] Since the subspaces are mutually orthogonal, The sample points drawn from the space can represent the uncertainty of the random variables in the space. The stratified sampling set without replacement for each orthogonal subspace becomes the sample library. The final sample set is the Latin hypercube uniformly distributed sampling points in the probability space. The probability density satisfies the linear relationship. For different probability distributions, the sample points of random parameters in the specific probability distribution space can be obtained by using equal probability density transformation, and finally the required seismic motion-structure random parameter sample set is obtained.

[0127] The above-mentioned application of the peak displacement envelope curve of the sliding layer of the high-speed railway system and the track irregularity prediction method considering the uncertainty of earthquake motion and pier height is used to predict the peak displacement envelope curve of the sliding layer and the track irregularity prediction of the high-speed railway system with a typical high-speed railway simply supported beam bridge as the benchmark structure.

[0128] The beneficial effects of the present invention are as follows:

[0129] 1) The present invention adopts a multimodal deep learning technology that integrates domain prior knowledge with structural features. Based on the prior domain knowledge of the response spectrum method and the feature tensor that integrates the pier height and seismic motion time history, a long sequence prediction framework TransTCN that combines the Transformer and TCN networks is constructed. This framework can effectively extract time series features and structural features, improve prediction accuracy and meet the training sample requirements at the same time, overcome the computational burden of purely physics-based proxy models and the modeling difficulties caused by changes in structural parameters, and significantly improve the fitting accuracy of pure data-driven models and reduce the demand for training data.

[0130] 2) The long sequence prediction framework TransTCN constructed by the present invention can accurately capture the complex spatiotemporal dependencies between time step features. Various classic neural network-based models were compared and ablation experiments were conducted on reliable training samples verified by shaking table tests, verifying the effectiveness and applicability of the RSM-based PDK method in improving the generalization performance of the network. TransTCN can effectively extract time series features and structural features, thereby improving prediction accuracy. Compared with the classic neural network models with better performance, the proposed model achieved a minimum prediction accuracy improvement of 7.1%. Under the same accuracy conditions, the training sample requirements decreased by 300%, which can provide new perspectives for regional earthquake risk assessment and performance-based seismic design methods.

[0131] 3) The present invention integrates prior knowledge of the target field to make up for the deficiencies of deep learning in interpretability, effectively reduce the data volume requirement, and embeds prior information such as control equations, physical laws, engineering theories, and expert experience into the data-driven model. While achieving data fitting, the prior knowledge is used to constrain the prediction results to conform to the physical mechanism. In earthquake engineering, the constrained model has stronger robustness and significantly reduces the demand for training data.

[0132] 4) The long sequence prediction framework model TransTCN constructed by the present invention, which combines the Transformer and TCN networks, integrates the advantages of TCN temporal convolution and the advantages of Transformer multi-head self-attention mechanism, and accurately captures the complex spatiotemporal dependencies between multiple time step features. The multimodal hybrid neural network model can effectively predict the seismic peak response and track irregularity of the track structure under the uncertainty of the bridge pier height of the high-speed rail system, and has significant advantages in calculation accuracy compared with other similar technologies; the spatial feature input of the superposition response spectrum method can significantly improve the performance of the model, and has potential advantages in dealing with regional earthquake loss assessment under structural randomness. The model of the present invention has significantly lower data requirements than other models, has better convergence and faster convergence speed, and realizes the prediction of the seismic peak response and track irregularity of the track structure under the uncertainty of the bridge pier height of the high-speed rail system, providing an effective calculation tool for real-time identification of regional high-speed rail system damage and regional structural seismic risk assessment, which helps to overcome the limitations of traditional finite element methods in large sample earthquake damage calculations. BRIEF DESCRIPTION OF THE DRAWINGS

[0133] Figure 1 This is a schematic diagram of the fusion of ground motion and structural characteristics;

[0134] Figure 2 Schematic diagram of TCN and transformer network structure; ((a) is the TCN residual block, (b) is the DCC network layer diagram, (c) is the transformer sub-model, and (d) is the multi-head attention structure);

[0135] Figure 3 This is a schematic diagram of the overall architecture of TransTCN;

[0136] Figure 4 Schematic diagram of the CRTSII track-bridge system structure and verification results; ((a) is the finite element diagram of the high-speed railway track-bridge system, (b) is the seismic experiment and seismic input, and (c) is the experimental verification result);

[0137] Figure 5 To select the response spectrum and average spectrum of the earthquake motion set;

[0138] Figure 6The structural seismic response obtained by nonlinear time history analysis of the finite element model established for the random parameter sample set input;

[0139] Figure 7 Prepare diagrams for training data;

[0140] Figure 8 is a comparison of model performance under different pier height distributions; (a) is a comparison of model performance under peak-type pier height distribution, (b) is a comparison of model performance under W-type pier height distribution, (c) is a comparison of model performance under valley-type pier height distribution, and (d) is a comparison of model performance under equal pier height distribution);

[0141] Figure 9 shows the performance comparison of the models under different data inputs. (Figure (a) shows the R of different models under different data inputs. 2 Indicator comparison, (b) is the MAE indicator comparison of different models under different data inputs, and (c) is the MSE indicator comparison of different models under different data inputs). DETAILED DESCRIPTION

[0142] The following will be combined with the embodiments and drawings to clearly and completely describe the technical solution of the present invention. Obviously, the described embodiments are only preferred embodiments of the present invention, not all embodiments, and are not intended to limit the present invention in other forms. Any technician familiar with the profession may use the disclosed technical content to make changes or modifications. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

[0143] Example 1

[0144] In order to overcome the computational burden of purely physics-based proxy models and the modeling difficulties caused by changes in structural parameters, and to significantly improve the fitting accuracy of pure data-driven models and reduce the demand for training data, this embodiment proposes a multimodal TransTCN fusion network embedded with domain prior knowledge to achieve a method for predicting peak displacement response and track irregularity of high-speed railways under uncertain pier height.

[0145] This embodiment takes a typical high-speed railway simply supported beam bridge as the research object, realizes the prediction of the peak displacement envelope curve of the sliding layer and the track irregularity of the high-speed railway system considering the uncertainty of earthquake motion and pier height, and compares it with other existing similar technologies, demonstrating the superiority of the model proposed in this embodiment in terms of computational efficiency and accuracy. The proposed method can provide technical support for the quantification of driving safety uncertainty in the high-speed railway network and the regional driving risk assessment.

[0146] First, this embodiment constructs a multimodal hybrid neural network model TransTCN embedded with domain prior knowledge; the domain prior knowledge is prior information including relevant control equations, physical laws, engineering theories and expert experience in the domain; the constructed multimodal hybrid neural network model TransTCN is a long sequence prediction framework combining Transformer and TCN networks, which includes a Transformer module and a TCN module; the TCN module is used to capture the complete temporal dependency, which includes multiple dilated causal convolutional layers and a cross-path layer, uses rectified linear units as activation functions, and batch normalization as convolution filters.

[0147] Then, the multi-modal input features of the time series based on the fusion of structural characteristics of earthquake motion and the spatial series based on the output peak displacement of the elastic response spectrum method are extracted; the pier height characteristics and earthquake motion characteristics are used as time series characteristics through dimension fusion to deal with time dependence; the analysis results of the elastic response spectrum method are used as spatial characteristics to deal with spatial dependence;

[0148] Finally, the extracted features are input into the constructed multimodal hybrid neural network model TransTCN to realize the prediction of the peak displacement envelope curve of the sliding layer and track irregularity of the high-speed railway system considering the uncertainty of ground motion and pier height.

[0149] The specific process is as follows:

[0150] 1. Data preparation

[0151] 1.1 Seismic data processing and pier height feature fusion

[0152] In typical earthquake damage classification or response prediction, the input sequence is only the earthquake time series or various time-frequency decomposition results of earthquake motion, and the prediction output is the node response or node damage state. When the same method is used to deal with earthquake damage prediction of buildings with longitudinally long structures such as high-speed railways, there is a probability of ignoring or underestimating the damage state of the structure; and building a neural network framework for multiple node responses at the same time will bring a lot of computational burden. The response spectrum method, which predicts the peak response of a multi-degree-of-freedom (MDOF) system by combining modal responses, has been widely recognized in practical applications because of its favorable compromise between simplicity, practicality and efficiency. However, this method has great limitations in calculating the nonlinear response of structures.

[0153] In order to effectively integrate the earthquake motion characteristics and the bridge pier height characteristics, this embodiment processes the bridge pier height characteristics and the earthquake motion characteristics respectively as follows:

[0154] The earthquake motion sequence is expressed as E = {e1, e2, …, e t}∈R t , where et is the seismic acceleration at each moment, and t is the time sequence number.

[0155] The heights of multiple piers of the target bridge are expressed as P = {p1, p2, ..., p s-1}∈R s-1 , p s-1 is the height of the pier and s is the number of bridge spans.

[0156] The output of the prediction target (taking the envelope of the peak displacement of the structure after the earthquake as an example) is O k ={O1,O2,…,Oα}∈Rα, where O k is the peak displacement of the output point, and α is the number of nodes at the predicted location of the structure.

[0157] Then, the multiplication fusion method is used to improve the interaction between features, thereby improving the model's ability to recognize complex features. The feature processing flow is as follows: Figure 1 As shown in Figure 2, the characteristic input of a single fused ground motion is expressed as:

[0158] PE in =PTE (1)

[0159] Where: P is the pier height sequence; E is the earthquake motion sequence; PE in represents input features; T represents transposition operation.

[0160] 1.2 Response spectrum method

[0161] The seismic design and assessment of structural systems are usually based on the peak control of the seismic response of force or displacement. The use of the modal superposition principle to calculate the potential peak response of a multi-degree-of-freedom system, namely the response spectrum method (RSM), has great development potential. However, in the risk assessment of major structures, the use of the RSM method is still limited. For example, the time of occurrence of the peak modal response will not be completely matched, and the peak response can only be approximated by modal combination, which obviously will have significant errors and ignore the historical information related to plastic deformation. In this regard, in this embodiment, it is incorporated into the neural network as expert knowledge to appropriately solve the above limitations. The details are as follows:

[0162] 1.2.1 Domain Prior Knowledge Based on Response Spectrum Method

[0163] For a multi-span high-speed railway track bridge system with any structure, its motion equation can be expressed as A spring-mass system with damping in degrees of freedom:

[0164]

[0165] Where:

[0166] M is the mass matrix of the multi-span high-speed railway track bridge system;

[0167] C is the damping matrix of the multi-span high-speed railway track bridge system;

[0168] K is the stiffness matrix of the multi-span high-speed railway track bridge system;

[0169] is the acceleration vector of the multi-span high-speed railway track bridge system;

[0170] is the velocity vector of the multi-span high-speed railway track bridge system;

[0171] x(t) is the displacement vector of the multi-span high-speed railway track bridge system;

[0172] P(t) is the equivalent load acting on the system.

[0173] Among them, C is the classic Rayleigh damping, and the equation can be naturally decoupled;

[0174] Under a given earthquake motion sequence, P(t) can be expressed as:

[0175]

[0176] Where: ι represents the influence vector, Represents ground acceleration.

[0177] Therefore, for a linear elastic system with multiple degrees of freedom, the system response can be expressed as a valid combination of multiple modal components as follows:

[0178]

[0179] Where: u(t) is the total response of the system; u n (t) is the nth-order modal response; is the static response of the nth mode; A n (t) is the pseudo acceleration response of the nth mode, N is the number of modes, and u represents the modal order.

[0180] Among them A n (t) is:

[0181]

[0182] In this formula, A n (t) is the pseudo-acceleration response of the nth mode; represents the square of the natural frequency of the nth mode; D n (t) is the displacement response of the system.

[0183] The static response of the nth modal for

[0184]

[0185] Where: n represents the modal participation factor; φ n The nth order mode shape vector;

[0186] Since the modal static response is related to the modal participation coefficient, modal frequency and modal vibration vector, combining equations (4)-(6), the system total response n(t) equation is transformed into:

[0187]

[0188] Obtaining the maximum structural response during the earthquake excitation period is a key step in the seismic design or seismic assessment of the structure, that is, solving:

[0189]

[0190] Among them, u no =Γ n φ n D n (t), represents the peak response of the nth mode, which can be easily obtained by response spectrum calculation.

[0191] Obtaining the maximum response from a time history analysis requires a lot of computational requirements, but the peak modal response obtained by combining the response spectrum can approximate the maximum peak response of the structure. It is worth noting that the modal peak responses usually do not occur at exactly the same time point, and the simplest approximation rule is Assuming that the modal peaks occur at the same time and direction, the approximate response is obtained by summing the absolute modal responses. This method is called the absolute sum (ABSSUM) modal combination rule, which usually provides an upper limit on the actual response. However, in structural design and evaluation, the ABSSUM rule is considered to be too conservative.

[0192] In addition, some studies have proposed a modal response hypothesis based on statistical independence, the root sum of squares (SRSS) rule, which can significantly reduce the calculation error of the ABSSUM rule when the modal frequencies of the structure are well separated:

[0193]

[0194] However, for structures with close modal periods, such as the high-speed railway track bridge system used in this embodiment, the correlation between the peak modal responses needs to be considered to prevent significant errors.

[0195] Therefore, this embodiment uses the perfect square combination (CQC) rule to more accurately predict the maximum response of the structure when the modal responses have significant cross-correlation:

[0196]

[0197] In the formula, l in Represents the correlation between the i-th and n-th modal responses.

[0198] This formula can be expanded to:

[0199]

[0200] In the CQC rule, the modal correlation coefficient l in It can be calculated by the following formula:

[0201]

[0202] In the above formula, u o is the maximum response (peak response) of the structure; N is the number of modes; u io The peak response of the ith mode; ζ i The damping ratio of the i-th order mode represents the ability of this mode to dissipate vibration energy; ζ n The damping ratio of the nth mode; where, represents the natural frequency ratio of the i-th mode to the n-th mode, ω i and ω n are the natural frequencies of the i-th mode and the n-th mode respectively.

[0203] This formula takes into account the relationship between different modal frequencies and damping ratios, improving the accuracy of the CQC rule. The input result of the response spectrum method is recorded as RS in .

[0204] 2. TransTCN prediction model

[0205] TCN networks and Transformers are widely used in time series tasks. In order to overcome the forgetting defects and insufficient local feature extraction capabilities of RNN-type networks in sequence data learning, this embodiment adopts a model that fuses TCN and transformer frameworks to effectively capture the correlation of multiple sequence inputs. Unlike the ordinary transformer framework, the TransTCN model described in this embodiment is an encoder-only framework; the nonlinear response of the structure is simultaneously affected by the structural features, time series features, and spatial features of the predicted position. In order to prevent the mutual influence between different features, it has two inputs, namely the time series matrix of the fused structural features and the calculation results of the response spectrum method. The TransTCN prediction model described in this embodiment, such as Figure 2 As shown, it includes Transformer module and TCN module.

[0206] Transformer modules, such as Figure 2 (c) is shown as being built on the basis of the Transformer model, which is used to capture the seismic characteristics and structural characteristics of the response spectrum method. The Transformer model is a sequence-to-sequence model based on the self-attention mechanism. It is a typical encoder-decoder structure. The encoder usually uses the self-attention mechanism, which enables it to be highly parallelized in the calculation process. Compared with the recurrent neural network (RNN) that calculates recursive results sequentially, the encoder structure can calculate faster when processing long sequences, significantly improving the efficiency of training and inference. In some time series tasks (such as classification, regression, etc.), the goal of the model is to extract features from the input sequence and make predictions directly without generating new sequences. In this case, only the encoder structure can extract the required features from the input data more directly, reducing the additional decoding steps, thereby simplifying the model and improving efficiency.

[0207] The Transformer module described in this embodiment includes a multi-head self-attention and a fully connected feedforward network layer. The input sequence first passes through an embedding layer, which encodes the position of the input sequence and converts it into a vector sequence, and then processes it through multiple stacked self-attention layers (multi-head self-attention). The core of the self-attention mechanism is that it can model the relationship between each element in the sequence and all other elements. This enables the encoder to effectively capture global contextual information when processing time series data, and is particularly effective in modeling long-term dependencies. This feature is crucial for capturing the seismic characteristics and response spectrum structural features of this embodiment.

[0208] Input TransTCN model features XS = {xs1, xs2, ..., xs t} is converted into three trainable linear mapping feature matrices by the embedding layer, named query key Sum Scaled Dot-Product Attention and softmax function are used to consider its bidirectional time dependency on the historical sequence. The self-attention matrix is ​​expressed as:

[0209]

[0210] Among them, xs t is the characteristic of time series t, n model ,m modelare the number of queries and the length of the input sequence in the attention module, respectively. k and d v are the feature dimensions of the query, key, and value matrices respectively. It is the scaling factor for optimizing training to adjust the calculation of the inner product to prevent the inner product from being too large. In self-attention, d k and d v The Softmax function is used to convert the scaled dot product result into a probability distribution, and T is the transposition operator.

[0211] Since single-head attention may have insufficient local feature extraction, the focused attention position may not be completely accurate. This embodiment uses a multi-head attention structure to weight the obtained results to form a multi-head attention mechanism, so that the model can jointly focus on features from different positions in different representation subspaces.

[0212] The multi-head attention structure increases the model accuracy by processing different features in layers, splitting the input into fixed-size segments, and key Sum Perform different linear transformation projections, and then calculate the attention on each segment in parallel. Combine h independent scaling dot product attention results through vector concatenation (connect the first digits of the vectors) and linear transformation and obtain the output value through linear transformation (see Figure 2 (d)), satisfying:

[0213] MultiHead(Q,K,V)=Concatenate(head1,…,head h )W o (14)

[0214] Where h represents the number of heads, Represents the multi-head attention weight, head h It represents the attention head, and Concatenate represents the concatenation operation. The purpose of concatenation is to enable the model to focus on different parts or different features of the input, so as to learn richer information.

[0215] For the hi-th attention head, a single attention is calculated through different weight matrices:

[0216]

[0217] in, represents the self-attention transformation weight, Attention is the self-attention calculation, d model It is the characteristic dimension of the entire model.

[0218] However, when performing long time series prediction, the decoder will greatly increase the calculation time. In addition, using different decoding methods during training and decoding may lead to problems such as low prediction accuracy or overfitting. Especially when the training data set is small, problems such as low prediction accuracy or overfitting will be more prominent.

[0219] In order to avoid the above problems, and to extract the dependencies between time and ensure accurate prediction, this embodiment only uses Transformer combined with TCN. The TCN module described in this embodiment is an encoder-only framework, which is a traditional convolutional neural network (CNN) variant designed specifically for efficient and effective processing of sequence data, and can effectively capture the complete time dependency. That is, by combining the TCN module to achieve point-by-point convolution for time series tasks.

[0220] The structure of the module described in this embodiment is as follows Figure 2 As shown in (a), it contains multiple dilated causal convolution (DCC) layers and a cross-layer path, using rectified linear unit (ReLU) as the activation function and batch normalization as the convolution filter. When the lengths of the input and output data are different, a 1×1 convolution is used as the cross-path layer.

[0221] In this embodiment, the dilated causal convolution is a key component of the TCN module. Unlike causal convolution, which can only expand its receptive field by increasing the kernel size or adding more layers, causal convolution only satisfies simple sequence mapping. The dilated convolution used in this embodiment enables the TransTCN prediction model to handle long sequence structures and avoids the convolution layer becoming too deep and difficult to train.

[0222] For a one-dimensional time series input With filters f:{1,2,…,ζ-1}, the dilated convolution operation F on the elements θ in the one-dimensional sequence can be expressed as:

[0223]

[0224] Among them, θ represents the time step to be processed, ci is the time step currently being processed, cd is the expansion factor used to control the size of the interval, ζ is the size of the filter, and * represents the convolution operation. is a one-dimensional time series input. As the number of convolutional layers increases, the dilation factor increases exponentially. The structure of the dilated causal convolution is shown below:

[0225] By adjusting the dilation factor, the amount of information received by the TCN can be controlled. The receptive field of the TCN can be calculated as:

[0226]

[0227] Among them, R field is the receptive field of TCN; N stack is the number of stacked TCN layers, that is, the number of stacked convolutional layers; is the size of the convolution kernel, and cd is the expansion factor of each convolution layer.

[0228] In order to shorten the training time and avoid the degradation problem caused by the deep network, the residual module is used to train the network. By stacking several TCN layers, a larger dilation factor can be used to obtain a larger receptive field. When the lengths of the input and output data are different, a 1×1 convolution is used as a cross-path layer. The calculation process of the residual block is as follows:

[0229]

[0230] in, Represents the feature representation learned by the DCC layer. It is the input and the output features obtained after the convolution operation of the DCC layer. These features can effectively represent the temporal information of the input sequence.

[0231] Based on the above complete TransTCN prediction model, such as Figure 3 As shown, TransTCN receives input PE in and RS in (respectively, the seismic structure fusion features and the response results based on the response spectrum method) and obtain the attention scores of each sequence point through multi-head attention reconstruction, output the attention tensor of the current sequence position, and perform tensor normalization and attention filtering. The output features are enriched with timing information through a two-layer DDC module, using the rectified linear unit (ReLU) as the activation function, and normalization is used as a convolution filter to further extract the tensor features of the corresponding sequence position. The model uses a residual module to avoid model degradation.

[0232] 3. Output layer

[0233] Huber Loss is used as the loss function. By fine-tuning the parameter δ, an effective combination of mean square error (MSE) and mean absolute error (MAE) is achieved, which can effectively reduce the sensitivity of outliers while maintaining differentiability to reduce the impact of training. Huber Loss is defined as a piecewise function:

[0234]

[0235] in, is the predicted value, is the true value, and δ is the adjustment coefficient, which determines the transition threshold of the loss function from quadratic to linear. When , the loss function is in the form of a quadratic function, which has a greater penalty on the predicted value and better smoothness and stability. On the contrary, the loss function becomes a linear function, which has a smaller penalty on the predicted value when the error is large, reducing the impact of outliers on the model.

[0236] By continuously adjusting δ to make the predicted output consistent with the actual output, the adjusted network can be used to realize the prediction of the peak displacement envelope curve of the sliding layer and track irregularity of the high-speed railway system considering the uncertainty of ground motion and pier height.

[0237] 4. Model training data

[0238] The typical high-speed railway simply supported beam bridge described in this embodiment is an existing model, such as Figure 4 As shown, it is a finite element model of the bridge structure developed in OpenSees. The model has geometric and material nonlinearities and can accurately represent the potential nonlinear behavior of the bridge system.

[0239] In the high-speed railway simply supported beam bridge described in this embodiment, Concrete01 material is used in the fiber section to simulate the behavior of concrete, while Steel02 material represents the force-displacement relationship of the steel bar. The Giuffre-Menegotto-Pinto model is used to consider cyclic loading and unloading and the Bauschinger effect. The bridge pier is simulated by the fiber section nonlinear unit of the displacement foundation. The two ends of the track are consolidated to simulate the constraint effect of the roadbed at both ends. Considering the pile-soil interaction, ZeroLength six-way spring is used to simulate the pile foundation. The stiffness is calculated according to the field conditions of the bridge: 2.41e9N / m, 2.32e9N / m, 1.87e10N / m, 2.55e11N / m, 1.42e11N / m, 1.42e11N / m. The main beam, base plate, track plate and rail are simulated by elastic beam units, and the bearing, sliding layer, mortar layer, shear groove, shear steel bar, side block and fastener are simulated by TwoNodeLink units.

[0240] 4.1 Earthquake Records and Uncertainty Parameter Sampling

[0241] In this embodiment, the seismic motion records used for training, verification and testing are obtained from the NGA-West2 strong earthquake database provided by the Pacific Earthquake Engineering Research Center NGA-West2 database. A total of 4459 complete ground motion records of historical earthquake events are collected from this database. These records are distributed in 1086 accelerometer sites of 78 events, covering different site conditions, different magnitudes, different stations and different PGA values.

[0242] In order to ensure that the sampling can fully reflect the uncertainty and prove the universality of the proposed method, it is costly to consider various types of uncertain parameters at the same time. Not considering or under-considering a certain type of earthquake will cause defects in the accuracy of the model. According to the provisions of China's "Railway Engineering Seismic Design Code", the seismic motion is selected, and the influence of seismic motion propagation path, site conditions and spectral characteristics is fully considered. The shear wave velocity of the soil layer is divided into four categories according to the site boundaries of the Chinese code, and the design response spectra under the corresponding site conditions are generated respectively. The 50 groups of seismic motions with the highest matching degree are selected for each type of response spectrum. The response spectrum and average spectrum of the seismic motion set are selected as follows Figure 5 shown.

[0243] Each horizontal acceleration record is processed as a separate record. The sampling frequency of all seismic records is uniformly adjusted to 0.02s. The collected seismic duration is 30s to meet the calculation accuracy requirements of high-speed railway bridge structures. The seismic site parameter is used as the selection parameter e1, and PGA (value range 0 to 0.8g) is used as the selection parameter e2. The random selection library E = [e1, e2] of seismic parameters is constructed. T , assuming it follows a uniform distribution.

[0244] Due to the constraints of terrain conditions, the height of bridge piers usually has significant uncertainty. The change of pier height significantly affects the mass, stiffness, and damping matrix of the structure, and then affects the post-seismic damage state of the bridge. The variability of bridge structure response is usually at the same level as the variability of structural parameters. It is of great significance to fully consider the uncertainty of pier height in the dynamic analysis of bridge structure for the seismic performance analysis of bridges. The pier height parameter is expressed as PH = [P1, P2, ..., P S-1 ] T .P S-1 is the height of pier S-1, S is the number of bridge spans, and it is assumed to obey the normal distribution.

[0245] In order to improve the representativeness of training samples and the coverage of parameter space, this embodiment obtains low-bias samples based on structured randomness based on Latin hypercube stratified sampling method to construct a training data sample library. T and the uncertain parameters of pier height PH=[P1,P2,…,P S-1 ] T Construct S+1 dimensional probability space R U , represents the total space containing the uncertainty of all random variables (ground motion and pier height parameters). Let ξ=S+1, which represents the probability space dimension of the combination of bridge structure and ground motion. For the ξ-dimensional random variable set The random variables include all the pier height parameters and ground motion parameters, which together define R uEach sample point in . Decompose it into P mutually non-intersecting orthogonal subspaces where a single subspace ξ j The dimensions satisfy:

[0246]

[0247] It means that the sum of the dimensions of each subspace is equal to the dimension ξ of the entire probability space, and the dimension of each subspace does not exceed ξ.

[0248] At the same time, the orthogonality condition should be met:

[0249]

[0250]

[0251] in, is an empty set, ∩ and are the intersection operation and the union operation of all subspaces, respectively. Equations (21) and (22) indicate that different subspaces are independent of each other, that is, there is no overlap between them, and the union of all subspaces is equal to the original probability space R U .

[0252] Since the subspaces are mutually orthogonal, The sample points drawn from the space can represent the uncertainty of the random variables in the space. The stratified sampling set without replacement for each orthogonal subspace becomes the sample library. The final sample set is the Latin hypercube uniformly distributed sampling points in the probability space. The probability density satisfies the linear relationship. For different probability distributions, the sample points of random parameters in the specific probability distribution space can be obtained by using equal probability density transformation, and finally the required seismic motion-structure random parameter sample set is obtained.

[0253] Taking the Latin hypercube sampling of seismic motion as an example, for different seismic motion zoning, Latin hypercube sampling is used to obtain the corresponding seismic motion area, seismic motion number and PGA. For all seismic motions in the selected area, one seismic motion is randomly sampled without replacement, and the seismic motion is amplitude modulated to the corresponding PGA size. The processed seismic motion is used as the seismic motion input of the finite element model.

[0254] The finite element model established by inputting the constructed random parameter sample set is used for nonlinear time history analysis to obtain the corresponding structural seismic response, such as Figure 6 In addition, in order to provide a more accurate prediction of the seismic performance of the structure, this embodiment also establishes a three-dimensional model of bidirectional input motion and response, and adopts a bidirectional earthquake input direction with a lateral to vertical ratio of 1:0.65.

[0255] Example 2

[0256] This embodiment uses the prediction method described in Example 1 to predict the lateral displacement peak response envelope curve of the sliding layer with a significant probability of damage in the track structure under earthquake and the track irregularity peak envelope curve that seriously threatens driving safety. The data preparation process is as follows: Figure 7 At the same time, the effect of the prediction method described in the embodiment is quantitatively analyzed, ablated and qualitatively evaluated in a comprehensive test scenario.

[0257] 1. Method Validation

[0258] Track structures are prone to damage during lateral earthquakes due to the low yield force of the bearings, which is reflected in large-scale damage to the sliding layer and significant track irregularity. Therefore, in order to reflect the practicality and potential value of the model, this embodiment uses two data sets, each with 2,000 data points, for training, focusing on the peak displacement envelope curve of the sliding layer of the CRTSII high-speed railway track-simply supported beam bridge under 9 different pier heights and the track irregularity prediction. These data contain potential earthquake risks under different site conditions.

[0259] For the finite element model running the complete time history record, select the load step where the peak displacement appears in the nonlinear time history analysis and extract the lateral peak displacement envelope curve of the sliding layer node For Node The lateral peak displacements of the left and right rails in the sliding layer are recorded as Left and right rail nodes respectively The peak displacement of the node, the peak track irregularity is recorded as TI = (R l +R r ) / 2.

[0260] In order to evaluate the performance of the prediction method described in Example 1, the overall data set is divided into training (80%), validation (10%) and test (10%) sets, and the data will be randomly shuffled before training to ensure fair comparison of the prediction results. The network is implemented using the matlab platform, and the training of the prediction model is performed on the NVIDIA GTX3090 GPU. The TransTCN model is trained for 200 epochs, the network uses a batch size of 128, and uses the Adam optimizer with an initial learning rate of 0.01. 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 a 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 every 10 epochs. An early stopping strategy is used and L2 regularization is set to prevent overfitting. The early stopping is set to stop the model training when there is no significant improvement in accuracy after 20 epochs, and the L2 regularization value is set to 0.001.

[0261] 2. Evaluation Method

[0262] In order to achieve quantitative evaluation, this embodiment uses the mean absolute error (MAE), the root mean square error (RMSE) and the coefficient of determination (R 2 ) is used as the evaluation indicator to measure the overall model performance. The formula is as follows:

[0263]

[0264] Where Ω is the sample size, is the predicted value, is the true value, It is the true value mean, and the indicator is calculated in m.

[0265] 3. Accuracy comparison

[0266] In order to demonstrate the superiority of the prediction method described in Example 1, this example uses a deep learning benchmark method that has been proven to have good results in the field of structural earthquake response prediction and earthquake damage prediction in recent years for comparison. The benchmark method used is as follows.

[0267] (1) Bayesian Bi-LSTM: A fast prediction method using a Bayesian self-optimizing bidirectional long short-term memory (Bi-LSTM) network is used to develop a fast prediction framework for the seismic response of the HSR rail-bridge system.

[0268] (2) AttLSTM: An attention-based long short-term memory neural network (AttLSTM) is used to learn dynamics from limited training data and predict bridge responses under unseen earthquakes. The proposed method with attention mechanism outperforms the compared state-of-the-art LSTM in terms of accuracy and reliability.

[0269] (3) 2D CNN: LSTM, WaveNet and 2D CNN were studied and compared in predicting the seismic time-history responses of three types of buildings and bridge structures. Among them, CNN showed good performance in predicting displacement responses compared with the other two methods.

[0270] (4) ConvLSTM: A deep learning method ConvLSTM for predicting the nonlinear response of multi-component structures, which can achieve indirect prediction of the nonlinear response of building structures and the structural bearing curve.

[0271] It is worth mentioning that although the above-mentioned benchmark methods have been widely proven to show excellent performance in node response prediction and damage prediction, they are still different from the solution direction of the method proposed in the present invention. At the same time, the above-mentioned benchmark methods are all aimed at deterministic structures. When the structure type changes, the network needs to be retrained to obtain effective prediction results. Therefore, in order to make the model comparison reasonable, during training, the seismic motion combined with structural measures adopts the fusion feature multi-input method of the present invention to achieve displacement prediction for different pier heights. The test results of different models are shown in Table 1 and Figures 8 to 9.

[0272] Table 1. Prediction accuracy of peak displacement envelope or track irregularity under different network models

[0273]

[0274] From the results in Table 1, it can be seen that the TransTCN network proposed in the present invention shows excellent performance in both the prediction of the sliding layer peak envelope diagram and the prediction of the track peak unevenness. The sliding layer prediction performance is slightly improved compared with the performance of several other networks. Compared with the best performing 2D CNN network, R2 is improved by about 0.6%, the root mean square error (RMSE) is reduced by 66.3%, and the mean absolute error (MAE) is reduced by 0.5%. The prediction of track peak unevenness is improved more significantly. Compared with the worst performing model Bi-LSTM, the R2 of the track peak unevenness prediction is improved by about 87.5%, the root mean square error (RMSE) is reduced by 51.3%, and the mean absolute error (MAE) is reduced by 92.2%. Compared with the best performing model 2D CNN, the R2 of the track peak unevenness prediction is improved by about 9.0%, the root mean square error (RMSE) is reduced by 9.0%, and the mean absolute error (MAE) is reduced by 78.2%.

[0275] The improvement of R2 indicates the model's ability to explain the data, reflecting the superiority of the model of the present invention in fitting the data. The lower RMSE value indicates that the deviation between the predicted value and the true value becomes smaller, which enhances the accuracy and reliability of the model. The lower MAE value indicates that the average deviation between the predicted value and the actual value is smaller, indicating that the model provides more accurate predictions as a whole, which fully proves the superiority of the proposed model.

[0276] Figure 7 The performance comparison of several selected models for track peak irregularity on 9 spans with different pier heights is shown. It can be seen that the prediction curve of the TransTCN model of the present invention is more consistent with the finite element calculation results in terms of track irregularity prediction accuracy under different terrain pier heights. Secondly, ConvLSTM and 2DCNN networks can also effectively predict track peak irregularity under some terrains, and other networks have obvious differences compared with numerical results. Compared with other models, the model proposed in this paper has significant advantages in prediction accuracy and prediction stability.

[0277] Figure 8 shows the track irregularity prediction R under different data input conditions. 2 , MAE, and MSE changes. It can be seen from the results in the figure that when the number of training data is small (less than 500), the R 2 The MAE and MSE of TransTCN rise rapidly, and TransTCN's MAE and MSE drop rapidly, showing its efficient learning ability and fast convergence ability under a small amount of data. Compared with other models (AttLSTM, BiLSTM, ConvLSTM, 2DCNN), TransTCN performs better in the initial stage and has a small prediction error. After the training data reaches 1000, TransTCN's R 2 The value tends to be stable and remains close to 1.0, indicating that its prediction accuracy is high under a large amount of data. MAE and MSE values ​​continue to remain at a low level, and compared with other models, its MAE value is the lowest. The MAE values ​​of other models have varying degrees of fluctuation and high errors in the stable area, while TransTCN has always maintained the lowest prediction error, indicating that it has a significant advantage in prediction accuracy.

[0278] From the above analysis, it can be seen that the prediction method of the present invention performs well under different training data scales. With a small amount of data, TransTCN can quickly learn and achieve high-precision prediction; with a large amount of data, TransTCN can maintain stable high performance, and R 2 The values, MAE and MSE values ​​are better than those of other comparison models. These results fully demonstrate the superiority of the TransTCN model in terms of prediction accuracy and robustness, as well as the superiority of data volume!

[0279] In general, the long sequence prediction framework TransTCN constructed by the present invention, which combines the Transformer and TCN networks, realizes the prediction of the seismic peak response of the track structure and the track irregularity under the uncertainty of the bridge pier height of the high-speed railway system by combining the calculation results of the response spectrum method. Specifically, the method of the present invention integrates the advantages of TCN temporal convolution and the advantages of Transformer multi-head self-attention mechanism, and accurately captures the complex spatiotemporal dependencies between multiple time step features. When evaluated on a high-speed railway track-bridge system dataset with two random bridge piers with different spans, the present invention achieved better results compared with existing methods.

[0280] The multimodal hybrid neural network model proposed in the present invention can effectively predict the peak response of the track structure and the track irregularity under the uncertainty of the bridge pier height of the high-speed railway system, and has a significant advantage in calculation accuracy compared with other similar technologies; the spatial feature input of the superposition response spectrum method described in the present invention can significantly improve the performance of the model, and has potential advantages in dealing with the regional earthquake loss assessment under random structure. In addition, the model of the present invention has significantly lower data requirements than other models, and has better convergence and faster convergence speed. When the number of local earthquakes is higher than 600, R2 is greater than 0.9.

[0281] In summary, the model and method of the present invention provide an effective calculation tool for real-time identification of regional high-speed rail system damage and regional structural seismic risk assessment, which helps to overcome the limitations of traditional finite element methods in large-sample earthquake damage calculations.

[0282] It is obvious to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential features of the present invention. Therefore, the embodiments should be regarded as exemplary and non-restrictive from any point of view. In addition, it should be understood that although this specification is described in accordance with the embodiments, it does not contain only one technical solution. This narrative of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in the embodiments can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for predicting peak displacement envelope curve of sliding layer and track irregularity of a high-speed railway system considering ground motion and uncertainty of pier height, characterized by: The steps include: 1) Construct a multimodal hybrid neural network model TransTCN that embeds domain prior knowledge; 2) Extract multi-modal input features from the time series of pier height characteristics fused with earthquake motion characteristics and the spatial series of peak displacement output based on elastic response spectrum method; The seismic motion characteristics and bridge pier height characteristics are used as time series characteristics through dimension fusion to deal with time dependence; the elastic response spectrum analysis results are used as spatial characteristics to deal with spatial dependence; 3) The multimodal input features extracted in step 2) are input into the multimodal hybrid neural network model TransTCN constructed in step 1) for processing, so as to realize the prediction of the peak displacement envelope curve and track irregularity of the high-speed railway system sliding layer considering the uncertainty of ground motion and pier height.

2. The method for predicting the peak displacement envelope curve of the sliding layer of a high-speed railway system and track irregularity considering the uncertainty of ground motion and pier height according to claim 1, characterized in that: In step 1), the multimodal hybrid neural network model TransTCN is a long sequence prediction framework combining Transformer and TCN networks, which includes a Transformer module and a TCN module; The Transformer module is used to capture the temporal characteristics of earthquake motion and the spatial structure characteristics of the response spectrum method, and includes an embedding layer, a multi-head self-attention layer, and a fully connected feedforward network layer; The TCN module is used to capture the complete temporal dependencies, which includes multiple dilated causal convolutional layers and a cross-path layer, and uses rectified linear units as activation functions and batch normalization as convolution filters.

3. The method for predicting the peak displacement envelope curve of the sliding layer of a high-speed railway system and track irregularity considering the uncertainty of ground motion and pier height according to claim 1, characterized in that: In step 2), The time series based on the fusion of seismic motion and structural features is a series obtained by fusion of seismic data processing and pier height features. The specific fusion process is as follows: The earthquake motion sequence is expressed as E = {e1, e2, …, e t }∈R t , where e t is the seismic acceleration at each moment, and t is the time sequence number; The pier height sequence is expressed as P = {p1, p2, ..., p s-1 }∈R s-1 , p s-1 is the height of the pier, s is the number of spans of the bridge; the predicted result output of the peak displacement envelope or track irregularity of the structure after the earthquake is O = {O1, O2, ..., O α }∈R α , where O k is the peak displacement of the output point, α is the number of nodes at the predicted location of the structure; Using multiplication fusion, the structural characteristic time series of a single fused ground motion is expressed as: ON in =P T E (1); Where: P is the pier height sequence; E is the earthquake motion sequence; PE in represents input features; T represents transposition operation.

4. The method for predicting the peak displacement envelope curve of the sliding layer of a high-speed railway system and track irregularity considering the uncertainty of ground motion and pier height according to claim 1, characterized in that: In step 2), The spatial sequence of peak displacement output based on elastic response spectrum method is the analysis result of integrating domain prior knowledge into neural network by using response spectrum method. The specific analysis process is as follows: For a multi-span high-speed railway track bridge system composed of any structure, its motion equation is expressed as A spring-mass system with damping in degrees of freedom: Where: M is the mass matrix of the multi-span high-speed railway track bridge system; C is the damping matrix of the multi-span high-speed railway track bridge system; K is the stiffness matrix of the multi-span high-speed railway track bridge system; is the acceleration vector of the multi-span high-speed railway track bridge system; is the velocity vector of the multi-span high-speed railway track bridge system; x(t) is the displacement vector of the multi-span high-speed railway track bridge system; P(t) is the equivalent load acting on the system; Among them, C is the classic Rayleigh damping, and the equation can be naturally decoupled; Under a given earthquake motion sequence, P(t) can be expressed as: Where: ι represents the influence vector, represents ground acceleration; For a linear elastic system with multiple degrees of freedom, the system response is expressed as an effective combination of multiple modal components: Where: u(t) is the total response of the system; u n (t) is the nth-order modal response; is the static response of the nth mode; A n (t) is the pseudo-acceleration response of the nth mode, N is the number of modes, n represents the modal order; Among them A n (t) is: Where: A n (t) is the pseudo-acceleration response of the nth mode; represents the square of the natural frequency of the nth mode; D n (t) is the displacement response of the system; The static response of the nth modal for Where: Γ n represents the modal participation factor, φ n The nth order mode shape vector; Since the modal static response is related to the modal participation factor, modal frequency and modal vibration shape vector; Combining equations (4)-(6), the system total response u(t) equation is transformed into: Where Γ n and φ n represent the modal participation factor and the nth-order mode shape vector respectively; Obtaining the maximum structural response during the earthquake excitation period is a key step in the seismic design or seismic assessment of the structure, that is, solving, Where: u no =Γnφ n D n (t), represents the peak response of the nth mode, obtained by response spectrum calculation; The correlation between the peak modal responses is taken into account to prevent significant errors, and the perfect square combination method is used to predict the maximum response of the structure when the modal responses have significant cross-correlation: In the formula, ρ in represents the correlation between the i-th and n-th modal responses; This formula can be expanded to: In the CQC rule, the modal correlation coefficient ρ in Calculated by the following formula: Where: u o is the maximum response of the structure, N is the number of modes, u io is the peak response of the ith mode, ζ i is the damping ratio of the i-th mode, which indicates the ability of this mode to dissipate vibration energy. ζ n is the damping ratio of the nth mode, represents the natural frequency ratio of the i-th mode to the n-th mode, ω i and ω n are the natural frequencies of the i-th mode and the n-th mode respectively.

5. The method for predicting peak displacement envelope curve of sliding layer and track irregularity of high-speed railway system considering ground motion and pier height uncertainty according to claim 1, characterized in that: In step 3), the features extracted in step 2) are input into the multimodal hybrid neural network model TransTCN constructed in step 1), and the specific processing is as follows: After the time series of structural characteristics based on earthquake motion fusion and the spatial series of peak displacement output based on elastic response spectrum method are input into the multimodal hybrid neural network model TransTCN, they first pass through the embedding layer of the Transformer module to encode the position of the input sequence and convert it into a vector sequence, and then process it through the multi-head self-attention layer to obtain the attention score of each sequence point and output the attention tensor of the current sequence position; Then, the complete temporal dependency is captured through the TCN module, that is, the attention tensor obtained by the Transformer module is normalized and filtered, and the output features are enriched with temporal information through multiple dilated causal convolutional layers, using rectified linear units as activation functions, and further extracting tensor features of corresponding sequence positions through normalization as convolutional filters; Huber Loss is used as the loss function, and the effective combination of mean square error and mean absolute error is achieved by fine-tuning the parameter δ. The output result is adjusted, and the adjusted network can be used to realize the prediction of the peak displacement envelope curve of the sliding layer and track irregularity of the high-speed railway system considering the uncertainty of ground motion and pier height.

6. The method for predicting the peak displacement envelope curve of the sliding layer and track irregularity of a high-speed railway system considering the uncertainty of ground motion and pier height according to claim 5, characterized in that: The processing process of inputting the time series of structural characteristics based on ground motion fusion and the spatial series of peak displacement output based on elastic response spectrum method into the Transformer module is as follows: Input TransTCN model features XS = {xs1, xs2, ..., xs t } is converted into three trainable linear mapping feature matrices by the embedding layer, named as: query key Sum Among them, xs t is the characteristic of time series t, n model , m model are the number of queries and the length of the input sequence in the attention module, respectively. k and d v are the feature dimensions of the query, key, and value matrices, respectively; The scaled dot product attention and softmax function are used to consider its bidirectional temporal dependency on the historical sequence. The self-attention matrix is ​​expressed as in, It is the scaling factor for optimizing training to adjust the calculation of the inner product to prevent the inner product from being too large. In self-attention, d k and d v Equal; T is the transposition symbol; Multiple queries key Sum Perform different linear transformation projections, and then calculate the attention on each segment in parallel. Combine h independent scaled dot product attention results through vector concatenation and linear transformation and obtain the output value through linear transformation, satisfying: MultiHead(Q,K,V)=Concatenate(head1,...,head h )W o (14); Where: h represents the number of heads, represents the multi-head attention weight, head h represents the attention head, Concatenate represents the concatenation operation; For the hi-th attention head, a single attention is calculated through different weight matrices: Where: represents the self-attention weight, represents the multi-head attention weight, Attention is the self-attention calculation, d model It is the characteristic dimension of the entire model.

7. The method for predicting the peak displacement envelope curve of the sliding layer and track irregularity of a high-speed railway system considering the uncertainty of ground motion and pier height according to claim 5, characterized in that: The complete time dependency capture process through the TCN module is as follows: One-dimensional time series input With filters f:{1, 2, ..., ζ-1}, the dilated convolution operation F on the elements θ in the one-dimensional sequence can be expressed as: Where: θ represents the time step to be processed; ci is the time step currently being processed; cd is the dilation factor used to control the size of the interval; ξ is the size of the filter; * represents the convolution operation; It is a one-dimensional time series input; The receptive field of TCN can be calculated as: Where: R field is the receptive field of TCN; N stack is the number of stacked TCN layers, that is, the number of stacked convolutional layers; is the size of the convolution kernel, cd is the expansion factor of each convolution layer; The multimodal hybrid neural network model TransTCN adopts a residual module to avoid model degradation. The calculation process of the residual block is as follows: Where: Represents the feature representation learned by the DCC layer; It is the input and the output features obtained after the convolution operation of the DCC layer. These features can effectively represent the temporal information of the input sequence.

8. The method for predicting peak displacement envelope curve of sliding layer and track irregularity of high-speed railway system considering ground motion and pier height uncertainty according to claim 7, characterized in that: The output layer of the multimodal hybrid neural network model TransTCN adopts Huber Loss as the loss function, which is defined as a piecewise function: Where: is the predicted value, is the true value, δ is the adjustment coefficient, which determines the transition threshold of the loss function from quadratic to linear; By continuously adjusting δ to make the predicted output consistent with the actual output, the adjusted network can be used to realize the prediction of the peak displacement envelope curve of the sliding layer and track irregularity of the high-speed railway system considering the uncertainty of ground motion and pier height.

9. The method for predicting peak displacement envelope curve of sliding layer and track irregularity of high-speed railway system considering ground motion and pier height uncertainty according to claim 1, characterized in that: The method also includes the step of training the multimodal hybrid neural network model TransTCN constructed in step 1), and the process of seismic records and uncertainty parameter sampling used in the training is: The seismic records used for training, verification and testing are matched with the design response spectra that fully consider the seismic propagation path, site conditions, spectral characteristics and soil shear wave velocity, and then the training data sample library is obtained based on the Latin hypercube stratified sampling method; The uncertainty parameter of the earthquake motion is E = [e1, e2] T and the uncertain parameters of pier height PH=[P1,P2,…,P S-1 ] T Construct S+1 dimensional probability space R U , represents the total space of uncertainties of all random variables including ground motion and pier height parameters; Let ξ = S + 1, which represents the probability space dimension of the combination of bridge structure and ground motion; For a ξ-dimensional random variable The random variables include all the bridge pier height parameters and ground motion parameters, which together define R u Each sample point in ; Decompose it into P mutually disjoint orthogonal subspaces where a single subspace ξ j The dimensions satisfy: It means that the sum of the dimensions of each subspace is equal to the dimension ξ of the entire probability space, and the dimension of each subspace does not exceed ξ; at the same time, the orthogonal condition should be satisfied: Where: is an empty set, ∩ and are the intersection operation and the union operation of all subspaces, respectively. Equations (21) and (22) indicate that different subspaces are independent of each other, that is, there is no overlap between them, and the union of all subspaces is equal to the original probability space R U ; Since the subspaces are mutually orthogonal, from the subspace The sample points drawn from the space can represent the uncertainty of the random variables in the space. The stratified sampling set without replacement for each orthogonal subspace becomes the sample library. The final sample set is the Latin hypercube uniformly distributed sampling points in the probability space. The probability density satisfies the linear relationship. For different probability distributions, the sample points of random parameters in the specific probability distribution space can be obtained by using equal probability density transformation, and finally the required seismic motion-structure random parameter sample set is obtained.

10. Application of the peak displacement envelope curve of the sliding layer of a high-speed railway system and the method for predicting track irregularity considering the uncertainty of ground motion and pier height according to any one of claims 1 to 9, characterized in that: It is used to predict the peak displacement envelope curve of the sliding layer and track irregularity of the high-speed railway system with a typical high-speed railway simply supported beam bridge as the benchmark structure.

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