Method for efficiently predicting deformation field of cross-fault deeply-buried pipeline under action of earthquake load

Abstract

The invention provides an efficient prediction method for a deformation field of a fault-crossing deeply-buried pipeline under the action of an earthquake load, and the method comprises the following steps: building a three-dimensional numerical model comprising a pipeline structure, a fault zone and a stratum, and applying the earthquake load to the bottom or side boundary of the three-dimensional numerical model in the form of an acceleration time history; generating a plurality of groups of input parameters by adopting Latin hypercube sampling, and inputting the input parameters into the three-dimensional numerical model for dynamic calculation to obtain deformation time history data; performing harmonic decomposition and time-frequency feature extraction on the deformation time history data to form a data set; establishing and training a multi-layer perceptron and Transform coupled prediction model based on the data set; and inputting to-be-predicted parameters into the prediction model to output a deformation field. Various influence factors such as pipeline geometric parameters, stratum mechanical parameters, fault geometric characteristics and seismic oscillation characteristics are considered, and the pipeline deformation response under the multi-parameter coupling effect can be comprehensively evaluated.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering technology, specifically to an efficient method for predicting the deformation field of deeply buried pipelines across faults under seismic loads. Background Technology

[0002] Fault displacement under seismic loads is characterized by suddenness, nonlinearity, and spatial heterogeneity, posing a serious threat to the safe operation of pipelines buried deep across faults.

[0003] The non-uniform ground motion and fault displacement caused by seismic loads can lead to significant additional deformation and internal force responses in pipelines. This impact depends not only on the intensity of the ground motion but also on a variety of factors, including the mechanical properties of the strata, the geometric characteristics of the fault (dip angle, thickness), the pipeline's burial depth, and its structural parameters. Near fault zones, seismic loads can induce strong bending, shearing, and elliptic deformation in pipelines. In severe cases, this can lead to pipe buckling instability, pipe-soil interface delamination, or damage to connections, potentially causing major engineering accidents such as water supply interruptions and oil and gas leaks, posing a significant threat to regional water supply security and energy supply guarantees.

[0004] Currently, in engineering practice, the finite element method or finite difference method (such as commercial software like ABAQUS and FLAC3D) is mainly used to analyze the dynamic response of buried pipelines under seismic loads. These numerical methods can accurately reflect the seismic wave propagation process, the heterogeneity of the strata, and the coupling effect of pipe-soil interaction, and have become the main technical means for studying the seismic performance of pipelines. However, traditional numerical simulation methods have the following significant shortcomings in engineering applications:

[0005] First, each complete three-dimensional dynamic time history analysis requires complex steps including geometric modeling, mesh generation, parameter assignment, boundary condition application, dynamic solution, and post-processing. When it is necessary to perform parameter sensitivity analysis or optimization design for different seismic intensities, different geological formations, and different pipeline parameters, conducting numerical simulations one by one is insufficient to meet the urgent needs of rapid engineering evaluation and decision support.

[0006] Secondly, existing research mainly focuses on calculating the stress, strain, and displacement responses at specific monitoring points or key local sections of the pipeline, lacking a systematic prediction method for the distribution characteristics of the pipeline's complete deformation field along the axial and circumferential directions. This localized analysis approach makes it difficult to fully grasp the overall deformation evolution of the pipeline and cannot provide sufficient technical support for seismic reinforcement and risk assessment of the entire pipeline.

[0007] Furthermore, in practical engineering, geological parameters, fault characteristic parameters, and seismic motion parameters all exhibit significant uncertainties, necessitating extensive analysis of parameter variations and operating conditions. Traditional numerical simulation methods face exponentially increasing computational costs when dealing with batch calculations involving multiple parameters and operating conditions, severely limiting their application in engineering uncertainty analysis and reliability assessment.

[0008] Finally, while traditional machine learning methods based on pure data can achieve rapid predictions, they often ignore the constraints of physical laws, resulting in significant defects in the prediction results in terms of temporal continuity, spatial consistency, and physical rationality, making it difficult to guarantee prediction accuracy and reliability.

[0009] In recent years, machine learning and surrogate modeling techniques have received widespread attention and application in geotechnical engineering and structural dynamics. By training on a limited number of high-precision numerical simulation samples, data-driven response prediction models can be constructed, enabling rapid estimation of structural responses and significantly reducing computational costs. However, existing machine learning prediction models suffer from the following limitations: First, the prediction objects are limited; existing models mostly predict responses for specific monitoring points or local sections, lacking a full-field prediction method capable of simultaneously predicting the spatiotemporal evolution characteristics of the complete deformation field along the axial and circumferential directions of the pipeline. Second, the ability to capture spatiotemporal correlations is insufficient; traditional fully connected neural networks or shallow machine learning models struggle to effectively capture the complex spatiotemporal evolution of pipeline deformation fields under seismic loading, resulting in significant deficiencies in temporal continuity and spatial consistency. Third, the integration of physical constraints is low; purely data-driven models often neglect the physical laws and mechanical constraints of structural deformation, leading to potentially physically unreasonable prediction results. Fourth, the generalization ability needs improvement; the prediction accuracy of models outside the training parameter range often drops significantly, limiting their widespread application in practical engineering.

[0010] Therefore, how to achieve efficient prediction of the full-field deformation time history of deeply buried pipelines across faults under seismic loads while maintaining high accuracy, and how to establish an intelligent prediction model that combines physical constraints, spatiotemporal correlation capture capabilities, and good generalization performance, has become a pressing technical problem to be solved in this field. Summary of the Invention

[0011] This invention proposes an efficient method for predicting the deformation field of deeply buried pipelines across faults under seismic loads, in order to solve the technical problems of low computational efficiency, insufficient full-field prediction capability, and difficulty in parametric analysis of traditional numerical simulation methods.

[0012] To address the aforementioned technical problems, this invention provides an efficient method for predicting the deformation field of deeply buried pipelines across faults under seismic loading, comprising the following steps:

[0013] Step S1: Establish a three-dimensional numerical model including the pipeline structure, fault zone and strata, and apply the seismic load to the bottom or side boundary of the three-dimensional numerical model in the form of acceleration time history.

[0014] Step S2: Use Latin hypercube sampling to generate multiple sets of input parameters and input them into the three-dimensional numerical model to perform dynamic calculations and obtain deformation time history data;

[0015] Step S3: Perform harmonic decomposition and time-frequency feature extraction on the deformed time history data to form a dataset;

[0016] Step S4: Based on the dataset, establish and train a prediction model that couples a multilayer perceptron and a Transformer;

[0017] Step S5: Input the parameters to be predicted into the prediction model to output the deformation field.

[0018] Preferably, the parameters of the pipeline structure include outer diameter D, wall thickness t, burial depth H, and pipeline elastic modulus E. p Pipeline structure Poisson's ratio v p ;

[0019] The parameters of the formation include the formation elastic modulus E. s Poisson's ratio of the formation v s , formation density ρ s Formation cohesion c s and the internal friction angle φ of the formation;

[0020] The parameters of the fault zone include a thickness of ,inclination The elastic modulus E of the fault zone f Poisson's ratio v of fault zone f Fault zone density ρ f Fault zone cohesion c f and the internal friction angle φ of the fault zone f .

[0021] Preferably, the input parameters include parameters of the pipeline structure, strata, fault zone, and seismic motion characteristics, wherein the seismic motion characteristics parameters include peak ground acceleration (PGA) and dominant frequency f. p and duration d .

[0022] Preferably, the dynamic calculation step includes:

[0023] The FISH language is used to write automated scripts to achieve parametric modeling, boundary condition application, and solution scheduling.

[0024] A data extraction program was written using a Python interface to automatically extract the time history of the radial displacement of the pipeline along the axial direction (z) and the circumferential direction (θ) throughout the entire process of seismic action. t represents time;

[0025] The radial displacement time history The deformation time history data is stored according to the working condition number.

[0026] Preferably, the harmonic decomposition step specifically includes:

[0027] For each time t i radial displacement Finite-order harmonic expansion:

[0028] ;

[0029] Obtain the harmonic coefficient sequence ,in Indicates the pipe expansion mode. and Indicates elliptic mode, and Represents asymmetric deformation modes; where

[0030] The time-varying amplitude value represents the expansion / contraction mode of the pipeline. and This represents the time-varying amplitude of the ellipticized mode. and Time-varying amplitude values ​​representing asymmetric deformation modes; modal basis functions and The truncation order m=0,2,3 remains constant.

[0031] Preferably, the method for time-frequency feature extraction includes: processing the harmonic coefficient sequence. Perform wavelet packet transform or Fourier transform to extract time-frequency domain feature parameters and construct deformable features.

[0032] Preferably, the structure of the prediction model coupled with the multilayer perceptron and the Transformer includes:

[0033] The multilayer perceptron encoder receives the input parameters and extracts a high-dimensional feature vector h. o ;

[0034] The one-dimensional Transformer encoder receives the high-dimensional feature vector h. o Learning harmonic coefficient sequences The spatiotemporal evolution law;

[0035] The one-dimensional Transformer encoder includes four encoding layers, each with four attention heads, a hidden dimension of 128, and uses GELU as the activation function.

[0036] The fully connected layer receives the output of the one-dimensional Transformer encoder and predicts the harmonic coefficients. ;

[0037] The predicted radial displacement is obtained using the harmonic reconstruction formula. .

[0038] Preferably, the training steps include:

[0039] Minimize the composite loss function using the Adam optimization algorithm:

[0040] ;

[0041] ;

[0042] in, This represents the overall deformation matching error. An axial smoothing constraint is used to constrain the continuity of the predicted deformation field along the axial direction. This is a time-smoothing constraint used to constrain the continuity of the predicted deformation field over time. and These represent the predicted and actual radial displacements, respectively. and These are the weighting coefficients for the axial smoothing constraint and the temporal smoothing constraint, respectively, used to adjust the contribution ratio of each loss in the overall training process; NKMT is the total number of spatiotemporal discrete points in the entire field.

[0043] Preferably, the deformation field includes the full-field radial displacement distribution at any given time. Peak deformation contour plot and ellipticity along the axial direction .

[0044] Preferably, the seismic load is applied using the equivalent free-field boundary method or the viscous boundary method to achieve wave input, and the acceleration time history a g (t) represents the measured seismic record, synthetic wave, or reflected correction wave.

[0045] Compared with the prior art, the beneficial effects of the present invention include at least the following:

[0046] This invention can predict the complete deformation field distribution of pipelines along the axial and circumferential directions, comprehensively revealing the overall deformation characteristics and local deformation concentration areas of pipelines under seismic loading. It effectively captures the complex spatiotemporal correlation of pipeline deformation fields under seismic loading, and the prediction results significantly outperform traditional machine learning methods in terms of temporal continuity and spatial consistency. The predicted deformation time-history curves are smooth and continuous, conforming to physical laws and accurately reflecting the entire process of seismic dynamics. By introducing axial smoothing and temporal smoothing constraints into the loss function, the invention ensures that the prediction results meet the continuity requirements of structural deformation, avoiding non-physical abrupt changes and oscillations, thus improving the physical rationality and reliability of the prediction results. Harmonic decomposition technology is used to compress the high-dimensional pipeline deformation field into a low-dimensional harmonic coefficient sequence, significantly reducing data dimensionality while retaining the main physical characteristics of the deformation field. This not only improves model training efficiency but also enhances model interpretability; each order of harmonic coefficient has a clear physical meaning, facilitating engineering applications and result analysis. Considering multiple influencing factors such as pipeline geometric parameters, stratum mechanical parameters, fault geometric characteristics, and seismic motion characteristics, the invention can comprehensively evaluate the pipeline deformation response under multi-parameter coupling.

[0047] In summary, the efficient prediction method for the deformation field of deeply buried pipelines across faults under seismic loads proposed in this invention solves the technical bottlenecks of low computational efficiency and insufficient full-field prediction capability of traditional numerical simulation methods. It provides an efficient, accurate, and reliable technical means for seismic design, risk assessment, and emergency decision-making of pipelines across faults, and has significant technological progress and broad engineering application prospects. Attached Figure Description

[0048] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention;

[0049] Figure 2 This is a schematic diagram of a three-dimensional numerical model according to an embodiment of the present invention;

[0050] Figure 3 This is a schematic diagram of discrete points of pipeline deformation field data near the fault in an embodiment of the present invention;

[0051] Figure 4 This is a schematic diagram of a spatiotemporal feature encoding pipeline deformation field prediction model based on the coupling of a multilayer perceptron and a Transformer, according to an embodiment of the present invention.

[0052] Figure labeling: 1-Fault zone; 2-Fault zone thickness; 3-Pipe thickness; 4-Pipe; 5-Structure to the left of the fault; 6-Structure to the right of the fault; 7-Pipe outer diameter; 8-Pipe burial depth; 9-Fault dip angle; 10-Seismic load p; 11-Discrete monitoring point of pipe deformation field; 12-Model input layer; 13-Neural network hidden layer; 14-MLP module; 15-Transformer encoding module. Detailed Implementation

[0053] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0054] like Figure 1 As shown in the figure, this invention provides an efficient method for predicting the deformation field of a deeply buried pipeline across a fault under seismic load, comprising the following steps:

[0055] Step S1: Establish a three-dimensional numerical model of the deep-buried pipeline across the fault.

[0056] A 3D numerical model of the deep-buried pipeline across a fault was established using 3D numerical modeling software (such as FLAC3D). The model mainly consists of four components: the pipeline structure, the strata to the left of the fault, the strata to the right of the fault, and the fault zone. Figure 2 As shown.

[0057] Key parameters of the pipeline structure include: outer diameter D, wall thickness t, burial depth H, and elastic modulus E. p Compared to Poisson's ratio v p .

[0058] Different mechanical parameters can be assigned to the strata on either side of a fault to simulate the heterogeneity of actual geological conditions. Stratigraphic parameters include: elastic modulus E. s Poisson's ratio v s Density ρ s Cohesion c s And the internal friction angle φ.

[0059] Fault zones, as weak interlayers within strata, exhibit significantly weaker mechanical properties than the adjacent intact strata. The geometric characteristics of fault zones include: a thickness of... ,inclination Elastic modulus E f Poisson's ratio v f Density ρ f Cohesion c f and internal friction angle φ f .

[0060] The seismic load is applied to the bottom or side boundaries of the model in the form of acceleration time history ag(t). To accurately simulate the propagation of seismic waves and boundary reflection effects, the seismic input uses the equivalent free-field boundary method or the viscous boundary method to realize wave propagation. The seismic motion can be measured seismic records, synthetic waves, or reflected corrected waves.

[0061] During the modeling process, it is necessary to refine the mesh of the pipelines and surrounding strata near the fault zone to improve computational accuracy. The mesh size should be selected to meet the accuracy requirements for seismic wave propagation.

[0062] Step S2: Determine the influencing parameters and perform Latin hypercube sampling

[0063] The deformation response of deeply buried pipelines across faults under seismic loading is influenced by a combination of factors, necessitating a systematic determination of the key input parameters affecting the deformation field distribution and their reasonable value ranges. These parameters can be categorized into four main types:

[0064] (1) Pipeline structural parameters: outer diameter D, wall thickness t, burial depth H, elastic modulus E p Compared to Poisson's ratio v p These parameters directly affect the stiffness characteristics and deformation capacity of the pipeline.

[0065] (2) Formation mechanical parameters: elastic modulus E s Poisson's ratio v s Density ρ s Cohesion c s And the internal friction angle φ. Formation parameters determine the propagation characteristics of seismic waves within the formation and the characteristics of soil-conduit interaction.

[0066] (3) Fault zone parameters: including thickness of ,inclination Elastic modulus E f Poisson's ratio v f Density ρ f Cohesion c f and internal friction angle φ f Fault zones, as weak interlayers in the strata, have a decisive influence on the spatial distribution of pipeline deformation fields due to their geometric and mechanical characteristics.

[0067] (4) Seismic motion characteristic parameters: including peak ground acceleration (PGA), dominant frequency f p and duration d These parameters characterize the intensity, spectral characteristics, and duration of ground motion, directly affecting the dynamic response characteristics of the pipeline.

[0068] The above parameters are combined to form the input parameter vector:

[0069] ;

[0070] To efficiently generate sample points with good distribution characteristics in the parameter space, the Latin hypercube sampling method is adopted. Compared with traditional random sampling or grid sampling, the Latin hypercube sampling method can achieve uniform coverage of the parameter space with a smaller number of samples, improving the representativeness of the dataset and the efficiency of model training.

[0071] The basic principle of Latin hypercube sampling is to divide the range of each parameter into N equal intervals (N being the number of samples), then randomly select a value within each interval, and combine the parameters through random permutations to ensure that the samples are evenly distributed and without repetition across all dimensions. Typically, the number of samples N should be chosen considering both the parameter dimensions and computational resources, generally ranging from 100 to 1000 sets. This invention preferably uses a sample size of 300-500 sets, which effectively balances computational cost and model accuracy.

[0072] Step S3: Conduct batch dynamic numerical experiments and data extraction

[0073] To improve the efficiency and automation of numerical experiments, this invention also provides a complete batch calculation and data extraction system.

[0074] (1) Development of automated modeling and calculation scripts

[0075] Automation scripts are written using the scripting languages ​​built into 3D numerical modeling software (such as FISH in FLAC3D) to automate the entire process of parametric modeling, boundary condition application, and solution scheduling. The automation scripts mainly consist of three subroutine modules:

[0076] Modeling subroutine: Based on the input parameter set X, this subroutine automatically generates a 3D numerical model with specific geometric features. It can automatically generate inclined fault planes based on the fault dip angle and fault zone thickness, and adaptively refine the mesh for pipelines and surrounding rock near the fault zone to ensure computational accuracy in critical areas.

[0077] The parameter assignment subroutine automatically assigns appropriate material parameters and constitutive models to strata, fault zones, and pipeline structures. This subroutine supports flexible switching between different constitutive models, allowing users to select an elastic model, a Mohr-Coulomb model, or other constitutive models based on the specific engineering requirements. Simultaneously, this subroutine is also responsible for applying seismic motion inputs, including reading acceleration time history data, setting boundary condition types, and defining damping parameters.

[0078] Batch Calculation and Monitoring Extraction Subroutine: This subroutine controls the cyclical operation under multiple working conditions, automatically performs dynamic time history calculations, and monitors and records the displacement response of key pipeline locations in real time during the calculation process. It extracts time history displacement data of pipeline wall nodes from preset monitoring points and stores it in an orderly manner according to the working condition number.

[0079] (2) Data extraction program development

[0080] By utilizing the data interface of 3D numerical modeling software (such as FLAC3D's Python interface), a dedicated data extraction program was written to achieve batch automatic extraction of pipeline deformation field data. This program can automatically read the displacement response of all discrete nodes on the pipeline wall throughout the entire seismic process after calculation. Figure 3 As shown, the time history of radial displacement along the axial direction z and the circumferential direction θ is extracted. and axial displacement Key response quantities, etc.

[0081] To facilitate subsequent data processing and model training, the extracted data is output as HDF5 or NPZ format files according to the load case number. Each data file contains: radial displacement field. axial displacement Sampling time series t i and the corresponding input parameter X i The HDF5 format features efficient data compression and fast reading capabilities, making it particularly suitable for storing and processing large-scale datasets.

[0082] Through the above-mentioned batch numerical experiments, a large number of pipeline deformation time history samples under different working conditions can be efficiently obtained, forming a complete pipeline deformation time history sample database, providing sufficient high-quality data support for subsequent machine learning model training.

[0083] Step S4: Data Feature Extraction and Compressed Representation

[0084] The time-history data of pipeline deformation under seismic loads has extremely high dimensionality. Directly using it for machine learning model training would face the curse of dimensionality, resulting in low training efficiency and insufficient model generalization ability. To address this, in one embodiment of the present invention, harmonic decomposition technology is used to perform low-dimensional compression representation of the pipeline deformation field, which significantly reduces the data dimensionality while preserving the main physical characteristics of the deformation field.

[0085] (1) Harmonic decomposition principle

[0086] As a cylindrical structure, the circumferential deformation of a pipe can be represented by a Fourier series. For any time t... i And axial position z, radial displacement of the pipe It can be expanded into a superposition of finite-order harmonics:

[0087] ;

[0088] in Indicates the pipe expansion mode. and Indicates elliptic mode, and Represents asymmetric deformation modes; where The time-varying amplitude value represents the expansion / contraction mode of the pipeline. and This represents the time-varying amplitude of the ellipticized mode. and Time-varying amplitude values ​​representing asymmetric deformation modes; modal basis functions and The truncation order m=0,2,3 remains constant.

[0089] The harmonic expansion order is set to m=0,2,3, thus retaining the three main modes of pipe expansion, ellipticization and asymmetric deformation, so as to achieve a low-dimensional compressed expression of the deformation of the whole field.

[0090] Harmonic analysis of discrete monitoring points along the circumference of the pipeline allows for the calculation of harmonic coefficients of various orders using the least squares method or Fast Fourier Transform (FFT). These harmonic coefficients are then combined to form a harmonic coefficient sequence.

[0091] .

[0092] (2) Time-frequency feature extraction

[0093] To further capture the frequency characteristics of the harmonic coefficients evolving over time, the harmonic coefficient sequence was analyzed. Perform time-frequency domain analysis. Wavelet Packet Transform (WPT) or Fourier Transform (FT) can be used to extract time-frequency domain feature parameters.

[0094] Wavelet packet transform can analyze signals simultaneously in both the time and frequency domains, making it suitable for processing non-stationary seismic response signals. Through multi-scale decomposition, energy distribution characteristics of different frequency bands can be extracted, constructing a richer spatiotemporal representation of the deformation field.

[0095] After harmonic decomposition and time-frequency feature extraction, the original high-dimensional spatiotemporal data is compressed into low-dimensional feature vectors, which not only preserves the main physical information of the deformed field, but also significantly reduces the data complexity.

[0096] Step S5: Establish a hybrid spatiotemporal feature coding prediction model

[0097] Traditional fully connected neural networks struggle to effectively capture the complex spatiotemporal correlations of pipeline deformation fields under seismic loading. Therefore, in one embodiment of this invention, a hybrid dynamic full-field prediction model coupling a multilayer perceptron (MLP) and a Transformer is proposed, as follows: Figure 4 As shown, this fully leverages the advantages of MLP in feature extraction and Transformer in sequence modeling.

[0098] (1) Overall Model Architecture

[0099] The prediction model consists of three main parts: a multilayer perceptron encoder (MLP-Encoder), a one-dimensional Transformer encoder, and a fully connected output layer.

[0100] Multilayer perceptron encoder (MLP-Encoder): Receives the influence parameter vector X defined in step S2 as input, and extracts a high-dimensional feature vector h through multilayer nonlinear transformation. o MLP-Encoders typically contain 3-5 hidden layers, with the number of neurons in each layer gradually increasing (e.g., 64→128→256), and the activation function used is ReLU or GELU. Through the deep nonlinear mapping of MLPs, the complex coupling relationships between various input parameters can be effectively captured.

[0101] One-dimensional Transformer encoder: Receives the high-dimensional feature vector h output by the MLP encoder. o Learning harmonic coefficient sequences Evolutionary patterns along the axial and temporal dimensions. The Transformer employs a self-attention mechanism, which can simultaneously focus on information from all positions in the sequence, effectively capturing long-distance dependencies, making it particularly suitable for processing spatiotemporal sequence data.

[0102] In this embodiment of the invention, the Transformer encoder includes four encoding layers, each with four attention heads and a hidden dimension of 128. The activation function used is GELU, which, compared to the traditional ReLU, has smoother gradient characteristics, which is beneficial for model training. The positional encoding uses learnable vectors, enabling adaptive learning of positional information and improving the model's ability to model different axial positions and time steps.

[0103] Fully connected output layer: Receives the output of the Transformer encoder and predicts the harmonic coefficient sequence through the fully connected layer. The design of the output layer needs to ensure that the output dimension matches the dimension of the harmonic coefficient sequence.

[0104] (2) Deformation field reconstruction

[0105] After obtaining the predicted harmonic coefficient sequence, the full-field radial displacement distribution of the pipeline is recovered using the harmonic reconstruction formula:

[0106] ;

[0107] This formula can quickly reconstruct the radial displacement of any circumferential position of a pipeline based on a finite number of harmonic coefficients, achieving an efficient mapping from low-dimensional features to a high-dimensional deformation field.

[0108] Step S6: Model Training and Physical Constraint Optimization

[0109] To improve the accuracy and physical rationality of the prediction model, one embodiment of the present invention designs a composite loss function that, while ensuring the accuracy of data fitting, introduces a physical constraint term to ensure the spatiotemporal continuity of the prediction results.

[0110] (1) Design of composite loss function

[0111] The total loss function is defined as:

[0112] ;

[0113] ;

[0114] in, The full-field deformation matching error is used to measure the difference between the predicted deformation field and the actual deformation field. and These represent the predicted and actual radial displacements, respectively. and These are the weighting coefficients for the axial smoothing constraint and the temporal smoothing constraint, respectively, used to adjust the contribution ratio of each loss in the overall training process; NKMT is the total number of spatiotemporal discrete points in the entire field.

[0115] An axial smoothing constraint is used to constrain the continuity of the predicted deformation field along the axial direction, avoiding non-physical abrupt changes. This is a time-smoothing constraint used to constrain the continuity of the predicted deformation field over time.

[0116] (2) Model training strategy

[0117] The Adam optimization algorithm was used for model training. The initial learning rate was set to 0.001, and a cosine annealing learning rate decay strategy was adopted to gradually reduce the learning rate during the training process.

[0118] The training and validation datasets are divided in an 8:2 ratio. During training, model performance is evaluated on the validation set after each epoch, and an early stopping strategy is used to avoid overfitting. Batch size is set to 32-64, and the number of training epochs is typically 100-300, with the final number of epochs determined based on the convergence of the loss on the validation set.

[0119] To improve the robustness and generalization ability of the model, data augmentation techniques can be used during training, such as adding small-amplitude random perturbations to the input parameters and randomly sampling the deformation field data.

[0120] Step S7: Rapid prediction and visualization output of pipeline deformation field under seismic loading conditions

[0121] Once the model is trained, it can be used for rapid prediction of new working conditions. For a given set of input parameters X, input it into the trained prediction model and output:

[0122] (1) Radial deformation distribution across the entire field at any time It can display the complete deformation field distribution of the pipeline at any time during the entire seismic process, including deformation characteristics along the axial and circumferential directions.

[0123] (2) Peak deformation cloud map: Extract the maximum radial displacement of each point of the pipeline throughout the entire time history to generate a peak deformation cloud map, which intuitively displays the maximum deformation area and the location of the dangerous section of the pipeline.

[0124] (3) Ellipticity along the axial direction Ellipticity is defined as the ratio of the difference between the maximum and minimum diameters of a pipe cross-section to its average diameter, and is an important indicator for evaluating the degree of pipe deformation. The ellipticity distribution curve along the axial direction can quantitatively assess the severity of deformation at different locations in the pipe, providing a basis for formulating seismic reinforcement schemes for pipes.

[0125] (4) Time history response of key sections: The deformation time history curves of key sections near the fault zone can be extracted to analyze the time evolution of pipeline deformation and identify possible resonance phenomena or dangerous moments.

[0126] The method proposed in this invention can meet the needs of rapid evaluation, parameter sensitivity analysis and optimization design in engineering while ensuring prediction accuracy.

[0127] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described; only preferred embodiments of the present invention are illustrated. The descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present invention. As long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification.

[0128] It should be noted that those skilled in the art can make various modifications and improvements without departing from the inventive concept, and these all fall within the scope of protection of this invention. Therefore, the scope of protection of this invention should be determined by the appended claims.

Claims

1. A highly efficient method for predicting the deformation field of a deeply buried pipeline across a fault under seismic loading, characterized in that: Includes the following steps: Step S1: Establish a three-dimensional numerical model including the pipeline structure, fault zone and strata, and apply the seismic load to the bottom or side boundary of the three-dimensional numerical model in the form of acceleration time history. Step S2: Use Latin hypercube sampling to generate multiple sets of input parameters and input them into the three-dimensional numerical model to perform dynamic calculations and obtain deformation time history data; Step S3: Perform harmonic decomposition and time-frequency feature extraction on the deformed time history data to form a dataset; Step S4: Based on the dataset, establish and train a prediction model that couples a multilayer perceptron and a Transformer; Step S5: Input the parameters to be predicted into the prediction model to output the deformation field.

2. The efficient prediction method for the deformation field of a deep-buried pipeline across a fault under seismic load as described in claim 1, characterized in that: The parameters of the pipeline structure include outer diameter D, wall thickness t, burial depth H, and pipeline elastic modulus E. p Pipeline structure Poisson's ratio v p ; The parameters of the formation include the formation elastic modulus E. s Poisson's ratio of the formation v s , formation density ρ s Formation cohesion c s and the internal friction angle φ of the formation; The parameters of the fault zone include a thickness of ,inclination The elastic modulus E of the fault zone f Poisson's ratio v of fault zone f Fault zone density ρ f Fault zone cohesion c f and the internal friction angle φ of the fault zone f .

3. The efficient prediction method for the deformation field of a deep-buried pipeline across a fault under seismic load as described in claim 1, characterized in that: The input parameters include parameters related to the pipeline structure, geological formation, fault zone, and seismic motion characteristics. The seismic motion characteristics parameters include peak ground acceleration (PGA) and dominant frequency f. p and duration d .

4. The efficient prediction method for the deformation field of a deep-buried pipeline across a fault under seismic load as described in claim 1, characterized in that: The steps for the dynamic calculation include: The FISH language is used to write automated scripts to achieve parametric modeling, boundary condition application, and solution scheduling. A data extraction program was written using a Python interface to automatically extract the time history of the radial displacement of the pipeline along the axial direction (z) and the circumferential direction (θ) throughout the entire process of seismic action. t represents time; The radial displacement time history The deformation time history data is stored according to the working condition number.

5. The efficient prediction method for the deformation field of a deep-buried pipeline across a fault under seismic load as described in claim 4, characterized in that: The specific steps of harmonic decomposition are as follows: For each time t i radial displacement Finite-order harmonic expansion: ； Obtain the harmonic coefficient sequence ,in Indicates the pipe expansion mode. and Indicates elliptic mode, and Represents asymmetric deformation modes; where The time-varying amplitude value represents the expansion / contraction mode of the pipeline. and This represents the time-varying amplitude of the ellipticized mode. and Time-varying amplitude values ​​representing asymmetric deformation modes; modal basis functions and The truncation order m=0,2,3 remains constant.

6. The efficient prediction method for the deformation field of a deep-buried pipeline across a fault under seismic load as described in claim 5, characterized in that: The method for time-frequency feature extraction includes: processing the harmonic coefficient sequence. Perform wavelet packet transform or Fourier transform to extract time-frequency domain feature parameters and construct deformable features.

7. The efficient prediction method for the deformation field of a deep-buried pipeline across a fault under seismic load as described in claim 1, characterized in that: The structure of the prediction model coupled with the multilayer perceptron and Transformer includes: The multilayer perceptron encoder receives the input parameters and extracts a high-dimensional feature vector h. o ; The one-dimensional Transformer encoder receives the high-dimensional feature vector h. o Learning harmonic coefficient sequences The spatiotemporal evolution law; The one-dimensional Transformer encoder includes four encoding layers, each with four attention heads, a hidden dimension of 128, and uses GELU as the activation function. The fully connected layer receives the output of the one-dimensional Transformer encoder and predicts the harmonic coefficients. ; The predicted radial displacement is obtained using the harmonic reconstruction formula. .

8. The efficient prediction method for the deformation field of a deep-buried pipeline across a fault under seismic load as described in claim 1, characterized in that: The training steps include: Minimize the composite loss function using the Adam optimization algorithm: ； ； in, This represents the overall deformation matching error. An axial smoothing constraint is used to constrain the continuity of the predicted deformation field along the axial direction. This is a time-smoothing constraint used to constrain the continuity of the predicted deformation field over time. and These represent the predicted and actual radial displacements, respectively. and These are the weighting coefficients for the axial smoothing constraint and the temporal smoothing constraint, respectively, used to adjust the contribution ratio of each loss in the overall training process; NKMT is the total number of spatiotemporal discrete points in the entire field.

9. The efficient prediction method for the deformation field of a deep-buried pipeline across a fault under seismic load as described in claim 1, characterized in that: The deformation field includes the global radial displacement distribution at any given time. Peak deformation contour plot and ellipticity along the axial direction .

10. The efficient prediction method for the deformation field of a deep-buried pipeline across a fault under seismic load as described in claim 1, characterized in that: The seismic load is applied using the equivalent free-field boundary method or the viscous boundary method to achieve wave input, and the acceleration time history a... g (t) represents the measured seismic record, synthetic wave, or reflected correction wave.

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