Railway subgrade performance evaluation method based on dynamic agent analysis
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SOUTHWEST JIAOTONG UNIV
- Filing Date
- 2026-04-23
- Publication Date
- 2026-05-29
AI Technical Summary
Existing methods for evaluating railway subgrade performance are costly and time-consuming, making it difficult to track and quantify subgrade performance changes in real time and accurately. Furthermore, numerical simulation consumes huge computational resources and cannot meet the needs of rapid evaluation. Existing data-driven methods are insufficient in identifying the evolution of soil mechanical parameters within the subgrade and lack effective closed-loop evaluation methods.
A deep learning proxy model integrating physical constraints is constructed, and combined with the ensemble Kalman filter algorithm, to realize the real-time mapping of subgrade soil parameters to displacement response. Through dynamic proxy analysis and finite element simulation, a comprehensive performance evaluation index and hierarchical early warning system are established.
It enables rapid analysis and performance classification early warning of railway subgrade under long-term cyclic load, improves computing efficiency, ensures the physical rationality of prediction results, and can perceive the internal mechanical state of the subgrade in real time, providing a scientific basis for operation and maintenance.
Smart Images
Figure CN122113671A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of railway subgrade monitoring technology, and specifically discloses a railway subgrade performance evaluation method based on dynamic proxy analysis. Background Technology
[0002] As the foundation structure beneath the rails, railway subgrades experience irreversible stiffness degradation under long-term, high-frequency cyclic loading by trains. This leads to problems such as severe and uneven deformation, threatening the safety and stability of train operation. Therefore, accurate assessment and dynamic early warning of the performance evolution of railway subgrades during long-term service are crucial for achieving intelligent operation and maintenance of railway lines.
[0003] Existing methods for evaluating roadbed performance typically rely on empirical engineering formulas, field exploration, and complex indoor and outdoor experimental analyses to determine roadbed material properties. This approach is not only costly and time-consuming, but also struggles to reproduce the complex stress states and long-term load histories observed in the field, making real-time, accurate tracking and quantification impossible. On the other hand, while numerical simulation using the finite element method can describe the long-term dynamic response and deformation evolution of the roadbed in detail, it consumes enormous computational resources and has low solution efficiency, failing to meet the needs of iterative optimization in engineering design or rapid evaluation during the operational phase.
[0004] In recent years, data-driven methods have shown potential in modeling complex nonlinear systems and have begun to be applied to the field of infrastructure condition prediction. However, existing methods mainly focus on predicting external response results and lack the ability to identify the evolution of soil mechanical parameters within the subgrade over time. At the same time, existing technologies still do not fully utilize the synergistic effect between real-time monitoring data, numerical simulation results, and performance evaluation indicators, and there is a lack of a closed-loop evaluation method that can effectively combine external monitoring response, internal mechanical state inversion, and long-term performance classification and early warning of the subgrade.
[0005] In view of this, the present invention provides a railway subgrade performance evaluation method based on dynamic proxy analysis. By constructing a deep learning proxy model that integrates physical constraints, the method realizes real-time mapping of subgrade soil parameters to displacement response. Combined with the ensemble Kalman filter algorithm, the method dynamically inverts the internal soil parameters of the subgrade based on field monitoring data. Finally, a comprehensive performance evaluation index and hierarchical early warning system based on time-varying parameters are established, providing efficient and reliable technical support for the intelligent operation and maintenance of railway subgrades. Summary of the Invention
[0006] The purpose of this invention is to provide a method for evaluating the performance of railway subgrade based on dynamic proxy analysis, addressing the problem of how to integrate large-scale numerical simulation data with field monitoring displacement data to achieve rapid analysis of the dynamic response of railway subgrade under long-term cyclic loading, dynamic identification of soil parameters, and performance classification and early warning, while balancing analytical efficiency and physical rationality. The specific solution is as follows: A method for evaluating railway subgrade performance based on dynamic surrogate analysis includes the following steps: S1: Obtain dynamic displacement monitoring data of surface nodes on the centerline of the railway subgrade, and clean the dynamic displacement monitoring data to obtain the cleaned subgrade displacement sequence. S2: Based on the sampling of roadbed stiffness parameters and finite element dynamic simulation, generate finite element dynamic simulation results; S3: Collect time-series data pairs from the finite element dynamic simulation results to obtain training samples; the time-series data pairs include soil mechanics time-varying parameters and subgrade displacement values. S4: Construct a spatiotemporal sequence dynamic surrogate model, and train the spatiotemporal sequence dynamic surrogate model with training samples to obtain the final spatiotemporal sequence dynamic surrogate model; S5: The final spatiotemporal sequence dynamic proxy model is used as the forward prediction model, and the cleaned subgrade displacement sequence is used as the predicted displacement sequence. The forward prediction model is inverted based on the predicted displacement sequence to obtain the dynamic inversion model of subgrade soil parameters. S6: Based on the dynamic inversion model of subgrade soil parameters, construct a comprehensive weighted displacement index, and establish a comprehensive performance evaluation index and hierarchical early warning system for subgrade based on the comprehensive weighted displacement index, and output the subgrade status identification results.
[0007] Furthermore, S2 includes: S21: Determine the time-varying parameters of soil mechanics and their value ranges; the time-varying parameters of soil mechanics include the elastic modulus and Poisson's ratio; S22: Sampling of time-varying soil mechanics parameters within the parameter value range to obtain multiple parameter combinations; S23: Construct a finite element model of the roadbed; the finite element model of the roadbed is used to simulate the long-term deformation process of the roadbed soil. S24: Input each set of parameters into the roadbed finite element model in sequence, perform dynamic simulation calculation, and obtain the finite element dynamic simulation results.
[0008] Furthermore, the range of values for the elastic modulus and Poisson's ratio is as follows: ; ; in, and These are the elastic modulus and Poisson's ratio of the l-th soil layer at the initial moment of the analysis, respectively. and These are the minimum and maximum elastic moduli of the l-th soil layer at the initial time, respectively; and These are the minimum and maximum Poisson's ratios of the l-th soil layer at the initial time, respectively. For the number of soil layers, ; This refers to the number of soil layers in the roadbed. Multiple parameter combinations are as follows: ; ; ; in, and These are the initial elastic modulus vector and initial Poisson's ratio vector of each soil layer in the nth group of parameters, respectively. and These are the elastic modulus and Poisson's ratio of the first soil layer of the nth model at the initial moment, obtained by the Latin hypercube sampling method. and These are the elastic modulus and Poisson's ratio of the second soil layer in the nth model at the initial moment, obtained by the Latin hypercube sampling method. and , respectively, represent the elastic modulus and Poisson's ratio of the Lth soil layer in the nth model at the initial moment, obtained by the Latin hypercube sampling method; n is the variable of the subgrade finite element model. N represents the total number of finite element models of the roadbed.
[0009] Furthermore, S3 includes: S31: Collect the time-varying parameters of soil mechanics and the displacement values of the subgrade from the finite element dynamic simulation results, and construct training samples; S32: Divide the training samples to obtain the training set and the test set.
[0010] 5. The railway subgrade performance evaluation method based on dynamic proxy analysis according to claim 1, characterized in that, step S4 includes: S41: Construct a spatiotemporal sequence dynamic proxy model; the input of the spatiotemporal sequence dynamic proxy model is a time series data pair, and the output is the roadbed displacement value; S42: Train the spatiotemporal sequence dynamic surrogate model using the training set in the training samples to obtain the trained spatiotemporal sequence dynamic surrogate model; S43: Test the trained spatiotemporal sequence dynamic surrogate model using the test set in the training samples to obtain the model performance, and optimize the trained spatiotemporal sequence dynamic surrogate model to obtain the final spatiotemporal sequence dynamic surrogate model.
[0011] Furthermore, the loss function for training the spatiotemporal sequence dynamic surrogate model is: ; ; ; ; ; in, The loss function used to train the spatiotemporal sequence dynamic surrogate model; This is the tradeoff coefficient between data fitting loss and physical constraint loss; The mean square error between the model's predicted values and the actual values from the finite element dynamic simulation. , and These are the weight coefficients for the mechanical consistency constraint, the time smoothness constraint, and the monotonicity constraint, respectively. for Constraints; For time-series smoothing constraints; This is a monotonicity constraint term; The number of samples in the training set is T; the time step length is n; and the variables in the roadbed finite element model are n. and These are the displacement values predicted by the dynamic surrogate model for the nth model at times t-1 and t, respectively; The displacement value is obtained from the finite element dynamic simulation calculation of the nth model at time t; t is the time variable. The number of soil layers is a variable; This refers to the number of soil layers in the roadbed. This represents the elastic modulus matrix of the l-th subgrade soil extracted by the nth model at time t. The Poisson's ratio matrix of the l-th subgrade soil extracted by the n-th model at time t; The optimization constraints for the spatiotemporal sequence dynamic surrogate model are as follows: ; in, This represents the number of CNN convolutional kernels. and The number of CNN convolution kernels The minimum and maximum values can be obtained; This represents the number of hidden units in the GRU. and These represent the number of hidden units in the GRU. The minimum and maximum values can be obtained; The learning rate; For learning rate The maximum value; The optimized function is: ; in, To optimize the function; is the number of samples in the test set; n is the variable in the roadbed finite element model.
[0012] Furthermore, S5 includes: S51: The final spatiotemporal sequence dynamic proxy model is used as the forward prediction model, and the subgrade displacement sequence is used as the predicted displacement sequence of the forward prediction model. The inversion elastic modulus and inversion Poisson's ratio of each layer of subgrade soil are obtained through inversion. S52: Based on the inverted elastic modulus and inverted Poisson's ratio, construct a dynamic inversion model of subgrade soil parameters; S53: Based on the roadbed displacement sequence, inverted elastic modulus and inverted Poisson's ratio, the dynamic inversion model of roadbed soil parameters is updated to obtain the parameter state vector of the soil. S54: Based on the soil parameter state vector, the dynamic inversion model of subgrade soil parameters is optimized to obtain the final dynamic inversion model of subgrade soil parameters.
[0013] Furthermore, the dynamic inversion model for subgrade soil parameters is as follows: ; ; in, In order to be in The elastic modulus vector obtained by inversion at time step; In order to be in The Poisson's ratio vector obtained by time-inversion; and The l-th soil layer is located at... The elastic modulus and Poisson's ratio obtained by inversion at each moment ; For the number of soil layers, This refers to the number of soil layers in the roadbed. The updated dynamic inversion model for subgrade soil parameters is as follows: ; ; in, Let h be the parameter state vector of the soil in the k-th set at time h; The predicted state vector of the soil in the k-th set at time h before updating the dynamic inversion model of subgrade soil parameters; This represents the actual monitored displacement in the roadbed displacement sequence; The displacement is the forward prediction obtained by the surrogate model for the k-th set; Kalman gain; This is the forward mapping function of the trained CNN-GRU spatiotemporal sequence dynamic surrogate model.
[0014] The optimized dynamic inversion model for subgrade soil parameters is as follows: ; ; ; ; in, To optimize the dynamic inversion model of subgrade soil parameters; These are the weighting coefficients for the prediction error term, the parameter prior constraint term, and the parameter stability constraint term, respectively. The root mean square error is the average error of the entire sample. For the prior deviation of the parameter; is the parameter stability index; h is the time variable; H is the monitoring duration; k is the indicator variable; K is the total number of indicators; Let h be the parameter state vector of the soil in the k-th set at time h; This is the transpose of the matrix; The second norm of a vector; This is the weight matrix; Let be the parameter state vector of the soil in the k-th set at time h-1.
[0015] Furthermore, S6 includes: S61: Based on the dynamic inversion model of subgrade soil parameters, calculate the overall equivalent elastic modulus and overall equivalent Poisson's ratio of the subgrade soil. S62: Based on the overall equivalent elastic modulus and the overall equivalent Poisson's ratio, construct the comprehensive weighted displacement index of the roadbed; S63: Based on the comprehensive weighted displacement index and the standard limit of subgrade displacement, a hierarchical early warning system is established to obtain the subgrade condition identification results.
[0016] Furthermore, the overall equivalent elastic modulus and the overall equivalent Poisson's ratio are: ; ; in, and These are the overall equivalent elastic modulus and the overall equivalent Poisson's ratio, respectively. For the number of soil layers, This refers to the number of soil layers in the roadbed. The thickness of the l-th soil layer; and These are the elastic modulus and Poisson's ratio of the l-th soil layer at time h, respectively. The comprehensive weighted displacement index is: ; in, For comprehensive weighted displacement index; and These are the overall equivalent elastic modulus and the overall equivalent Poisson's ratio under the initial state of the roadbed, respectively. The monitored displacement of the roadbed at time h; The roadbed displacement limit was determined according to engineering specifications; , and The weighting coefficients for the first, second, and third entropy values are as follows: ; ; ; ; in, A standardized vector; This represents the percentage of the k-th indicator. Let h be the standardized value of the k-th index at time h; h is a time variable; Let ln be the information entropy of the k-th index; ln is the logarithmic function. The entropy value weight of the k-th indicator; For monitoring duration.
[0017] The present invention has the following advantages and beneficial effects: This invention constructs a CNN-GRU spatiotemporal sequence dynamic surrogate model that integrates physical constraints, which improves the computational efficiency of long-term roadbed dynamic simulation by more than two orders of magnitude, while ensuring the physical rationality of the prediction results, thus solving the problem of low computational efficiency of traditional numerical methods.
[0018] This invention employs an ensemble Kalman filter algorithm combined with a dynamic surrogate model to achieve dynamic inversion of subgrade internal soil parameters based on field monitoring displacement data. It can perceive the internal mechanical state of the subgrade in real time, overcoming the shortcomings of existing data-driven methods that can only predict external responses.
[0019] This invention establishes a comprehensive weighted displacement index and a three-level early warning system based on time-varying soil parameters, transforming complex mechanical states into simple and intuitive evaluation indicators and early warning signals. This achieves a direct leap from data analysis to maintenance decision-making, providing a scientific basis for the forward-looking maintenance of railway subgrades. Attached Figure Description
[0020] Figure 1 An exemplary flowchart of a railway subgrade performance evaluation method based on dynamic proxy analysis provided by the present invention; Figure 2 This is an exemplary flowchart for obtaining the spatiotemporal sequence dynamic proxy model provided by the present invention. Detailed Implementation
[0021] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.
[0022] like Figure 1 As shown, the present invention discloses a method for evaluating the performance of railway subgrade based on dynamic surrogate analysis, which specifically includes the following steps: S1: Obtain dynamic displacement monitoring data of surface nodes on the centerline of the railway subgrade, and perform data cleaning on the dynamic displacement monitoring data to obtain the cleaned subgrade displacement sequence.
[0023] Displacement response monitoring was performed on the railway subgrade structure, and the monitoring time for the surface nodes along the subgrade centerline was [duration missing]. Horizontal displacement data sequence The data was then processed to remove outliers, resulting in a cleaned time-series displacement sequence. .
[0024] S2: Based on random sampling of roadbed stiffness parameters and automated scripts, parametric finite element dynamic simulation calculations are performed to generate finite element dynamic simulation results. Specifically, the following steps are included: S21: Determine the key time-varying soil mechanical parameters affecting the long-term dynamic response of the subgrade. The parameter range in the structural parameter design space is determined based on the survey report and recommended values in the specifications. This range includes both upper and lower bounds. For example, elastic modulus and Poisson's ratio are selected as key soil parameters affecting the long-term dynamic response of the subgrade, and their upper and lower bounds at the initial moment are determined. Elastic modulus characterizes the stiffness of the soil under small strain and is a key parameter affecting the amplitude of the dynamic response and displacement calculations. Its value often varies significantly with depth, overconsolidation ratio, and water content, and must cover most possible stiffness states of the stratum. Poisson's ratio reflects the lateral deformation capacity of the soil under stress. During long-term cyclic loading and accompanying drainage consolidation, changes in effective stress lead to a decrease in Poisson's ratio. Taking into account the subgrade survey report, specification design requirements, the elastoplasticity of the soil skeleton, and some drainage conditions, a range of variation is set to cover typical cases ranging from near-elastic to considering plastic volume changes.
[0025] ; ; in, , The initial time for the analysis is the elastic modulus and Poisson's ratio of the l-th soil layer. , Let these be the minimum and maximum elastic moduli of the l-th soil layer at the initial moment. , The minimum and maximum Poisson's ratios of the l-th soil layer at the initial time are given. This represents the number of soil layers in the roadbed.
[0026] S22: Using the Latin hypercube sampling method, N sets of parameter combinations with good space-filling properties are generated within the parameter value range.
[0027] To ensure uniform coverage of the entire parameter space and avoid clustering issues inherent in simple random sampling, a Latin hypercube sampling method is used to generate N parameter combinations. This approach uses fewer samples to more efficiently characterize parameter uncertainty and reduces computational costs. The generated nth sample combination... : ; ; ; in, and These are the initial elastic modulus vector and initial Poisson's ratio vector of each soil layer in the nth sample group, respectively. , The elastic modulus and Poisson's ratio of the l-th soil layer in the n-th model obtained by the Latin hypercube sampling method at the initial moment are used as the initial parameter values for modeling.
[0028] S23: Establish a finite element model of the roadbed, set a fixed bottom boundary and lateral constraint boundary in the model, apply the equivalent dynamic load of the train, set the analysis time T, and simulate the long-term deformation process of the roadbed soil.
[0029] S24: Parametric finite element dynamic simulation based on random parameter combinations is performed. Each set of parameter combinations is sequentially input into the roadbed finite element model, and dynamic simulation calculations are executed to obtain the finite element dynamic simulation results. For example, the finite element software can be automatically and cyclically called by a control program, sequentially inputting N sets of parameter samples. As input, perform N dynamic simulation calculations to obtain the finite element dynamic simulation results.
[0030] S3: Based on the finite element dynamic simulation results, time-series data pairs from the finite element dynamic simulation results are collected to obtain training samples; the time-series data pairs include time-varying parameters of soil mechanics and subgrade displacement values. Specifically, the following steps are included: S31. For the finite element simulations of the N models completed in S2, the time-varying parameters of soil mechanics and the subgrade displacement values in the finite element dynamic simulation results are collected at equal time intervals T to construct training samples. At each time step, the elastic modulus and Poisson's ratio of each soil layer are updated based on the material state variables during the finite element calculation, and used as the time-varying parameters of soil mechanics for that time step. The elastic modulus and Poisson's ratio parameter matrices extracted from the nth finite element simulation model are as follows: ; ; in, ; and These are the elastic modulus matrix and Poisson's ratio matrix of the nth model out of a total of N finite element dynamic simulation models. and These are the nth finite element model and their respective... The elastic modulus and Poisson's ratio of a soil layer at time t.
[0031] For the nth finite element dynamic simulation model, extract the horizontal displacement of the surface nodes along the roadbed centerline. : ; in This is the displacement vector of the railway subgrade for the nth model; its elements are... It is the horizontal displacement of the surface node of the roadbed centerline at time t for the nth model.
[0032] Construct the parameter matrix into a time series data pair This reflects the instantaneous stiffness characteristics of the soil as a whole after the nth finite element dynamic simulation model has undergone a certain load history and creep.
[0033] S32. Extract data from all N finite element models The dataset is randomly divided into a training set and a test set in a 70%:30% ratio to form a complete dataset.
[0034] S4: Construct and train a spatiotemporal sequence dynamic surrogate model that incorporates physical constraints to obtain the final spatiotemporal sequence dynamic surrogate model, and complete the real-time mapping of soil parameters to displacement response.
[0035] S41. Construct a CNN-GRU spatiotemporal sequence dynamic surrogate model. The spatiotemporal sequence dynamic surrogate model adopts a CNN-GRU hybrid architecture, where the CNN part acts as a feature extractor and the GRU part acts as a temporal modeler, learning the evolution of parameters and horizontal displacement over time. The input tensor of the dynamic surrogate model is... The output tensor is ,in This represents the number of time-series data points in the training set.
[0036] S42. Using the training set from the training samples, the spatiotemporal sequence dynamic surrogate model is trained under supervision using a loss function that incorporates a physical loss term. When the loss value converges, the spatiotemporal sequence surrogate model completes the prediction and solution of the problem, resulting in a well-trained spatiotemporal sequence dynamic surrogate model. The loss function for training the spatiotemporal sequence dynamic surrogate model is as follows: Figure 2 As shown, it is defined as the weighted sum of the data fitting loss and the physical regularization loss term: ; ; ; ; ; in The mean square error between the model's predicted values and the actual values from the finite element dynamic simulation. for Constraints are used to ensure that the displacement prediction results are consistent with the changing trends of soil stiffness parameters. This is a temporal smoothing constraint term to ensure the temporal continuity of displacement evolution; This is a monotonicity constraint term to suppress non-physical bounce phenomena and make the results conform to the engineering characteristics of monotonic growth of long-term displacement; T is the time step length. Let n be the displacement value predicted by the dynamic surrogate model for the nth model at time t. Let n be the displacement value predicted by the dynamic surrogate model for the nth model at time t-1; The displacement value extracted from the nth model at time t by finite element dynamic simulation calculation; This represents the elastic modulus matrix of the l-th subgrade soil extracted by the nth model at time t. The Poisson's ratio matrix of the l-th subgrade soil extracted by the n-th model at time t; This is a tradeoff coefficient between data fitting loss and physical constraint loss, used to adjust the model's ability to fit finite element dynamic simulation data and its degree of satisfaction with physical constraints. , , These are the weighting coefficients for the mechanical consistency constraint, the time smoothing constraint, and the monotonicity constraint, respectively, used to adjust the contribution of different physical constraints to the total loss function.
[0037] S43. Select optimization parameters The trained spatiotemporal sequence dynamic surrogate model is tested using the test set from the training samples to obtain its performance. The trained model is then optimized to obtain the final spatiotemporal sequence dynamic surrogate model. The number of CNN convolution kernels, This represents the number of hidden units in the GRU. This is the learning rate.
[0038] in The optimization constraints are: ; in , The number of CNN convolution kernels The minimum and maximum values are taken. , These represent the number of hidden units in the GRU. The minimum and maximum values are taken. For learning rate The maximum value.
[0039] To evaluate the ability of the CNN-GRU dynamic surrogate model to approximate the finite element dynamic-creep response, the average root mean square error of the full sample was selected as the model performance evaluation index, and an optimization function was constructed: ; S5: The final spatiotemporal sequence dynamic proxy model is used as the forward prediction model, and the cleaned subgrade displacement sequence is used as the predicted displacement sequence. The forward prediction model is inverted based on the predicted displacement sequence to obtain the dynamic inversion model of subgrade soil parameters.
[0040] S51: The final spatiotemporal sequence dynamic (CNN-GRU) surrogate model is used as the forward prediction model, and the subgrade displacement sequence is used as the predicted displacement sequence of the forward prediction model. The inversion elastic modulus and inversion Poisson's ratio of each layer of subgrade soil at the current moment are obtained through inversion.
[0041] S52. Based on the inverted elastic modulus and inverted Poisson's ratio, a dynamic inversion model for subgrade soil parameters using ensemble Kalman filtering (EnKF) is constructed for the inversion of time-varying mechanical parameters of railway subgrades. The subgrade soil state vector (time-series data pair) is defined at time h. ,in ; ; Where L represents the number of subgrade soil layers; , The l-th soil layer is located at... The elastic modulus and Poisson's ratio obtained by inversion at each time step, where .
[0042] S53: Based on the subgrade displacement sequence, inverted elastic modulus, and inverted Poisson's ratio, the dynamic inversion model of subgrade soil parameters is updated to obtain the soil parameter state vector. For example, K set members are generated by sampling from the prior distribution obtained from geological survey data. For each time step h, perform the EnKF update step: ; ; in, Let h be the parameter state vector of the soil in the k-th set at time h; To update the predicted state vector of the soil in the k-th set at time h before EnKF updates; This refers to the actual monitored displacement; The displacement is the forward prediction obtained by the surrogate model for the k-th set; For Kalman gain, This is the forward mapping function of the trained CNN-GRU spatiotemporal sequence dynamic surrogate model.
[0043] S54: Based on the soil parameter state vector, the dynamic inversion model of subgrade soil parameters is optimized to obtain the final dynamic inversion model of subgrade soil parameters.
[0044] To ensure that the inversion results are numerically stable and physically reasonable, an optimization objective function is constructed to optimize the inversion model and find the optimal hyperparameters. ,in To observe the noise variance, The variance of the model error. For the size of the EnKF set, These are the prior constraint weights.
[0045] The objective function is optimized using... Parameter prior deviation and parameter stability index Construct a multi-objective optimization function: ; ; ; ; in, To optimize the dynamic inversion model of subgrade soil parameters; These are the weighting coefficients for the prediction error term, the parameter prior constraint term, and the parameter stability constraint term, respectively, used to adjust the contribution of different optimization objectives in the inversion process; The root mean square error is the average error of the entire sample. For the prior deviation of the parameter; is the parameter stability index; h is the time variable; H is the monitoring duration; k is the indicator variable; K is the total number of indicators; Let h be the parameter state vector of the soil in the k-th set at time h; Let h be the parameter state vector of the soil in the k-th set at time h-1; This is the transpose of the matrix; The second norm of a vector; Here is the weight matrix: ; in , Let be the a priori elastic modulus and a priori Poisson's ratio of the l-th soil layer.
[0046] S6: Based on the dynamic inversion model of subgrade soil parameters, construct a comprehensive weighted displacement index, and based on the comprehensive weighted displacement index, establish a comprehensive performance evaluation index and hierarchical early warning system for subgrade based on time-varying soil parameters, and output the subgrade state identification results.
[0047] S61: Calculate the overall equivalent elastic modulus of the subgrade soil based on the dynamic inversion model of subgrade soil parameters. and the overall equivalent Poisson ratio .
[0048] The L-layer soil parameters obtained from the S5 inversion were used to calculate the overall equivalent elastic modulus at time h, which reflects the overall stiffness and deformation characteristics of the subgrade. and the overall equivalent Poisson ratio .
[0049] ; ; in The thickness of the l-th soil layer; , Let be the elastic modulus and Poisson's ratio of the l-th soil layer at time h.
[0050] S62: Based on the overall equivalent elastic modulus and the overall equivalent Poisson's ratio, construct the comprehensive weighted displacement index of the roadbed. : ; in, , The overall equivalent elastic modulus and overall equivalent Poisson's ratio of the roadbed under the initial state; The monitored displacement of the roadbed at time h; The roadbed displacement limit was determined according to engineering specifications; , , The entropy weighting coefficients are calculated using the entropy method: ; ; ; ; in, , , These are the standardized values of the first, second, and third indicators at time h, respectively. This represents the percentage of the k-th indicator. Let h be the standardized value of the k-th index at time h; The information entropy of the k-th indicator; The entropy value weight of the k-th indicator; For monitoring duration.
[0051] S63: Based on a comprehensive weighted displacement index and the standard limits for subgrade displacement, a hierarchical early warning system is established to obtain subgrade condition identification results. For example, after determining the weights of each risk index, the standard limits for subgrade displacement are obtained by combining engineering practice experience and reliability theory. And obtained through the inversion model constructed using S5 The overall equivalent elastic modulus of the roadbed was calculated. and the overall equivalent Poisson ratio Substituting into the comprehensive weighted displacement index, we obtain the following calculation: : ; Therefore, a three-level evaluation and early warning system for roadbed performance is established, as shown in Table 1.
[0052] Table 1. Three-level evaluation and early warning system for roadbed performance Based on engineering experience and reliability analysis, the early warning threshold is set at 60% of the critical state to provide an early warning buffer. , .
[0053] This system transforms complex mechanical states into simple indicators and early warning signals, enabling a leap from data analysis to maintenance decision-making.
[0054] S64: Complete the subgrade condition identification based on the comprehensive weighted displacement index.
[0055] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for evaluating the performance of railway subgrade based on dynamic surrogate analysis, characterized in that, Includes the following steps: S1: Obtain dynamic displacement monitoring data of surface nodes on the centerline of the railway subgrade, and clean the dynamic displacement monitoring data to obtain the cleaned subgrade displacement sequence. S2: Based on the sampling of roadbed stiffness parameters and finite element dynamic simulation, generate finite element dynamic simulation results; S3: Collect time-series data pairs from the finite element dynamic simulation results to obtain training samples; the time-series data pairs include soil mechanics time-varying parameters and subgrade displacement values. S4: Construct a spatiotemporal sequence dynamic surrogate model, and train the spatiotemporal sequence dynamic surrogate model with training samples to obtain the final spatiotemporal sequence dynamic surrogate model; S5: The final spatiotemporal sequence dynamic proxy model is used as the forward prediction model, and the cleaned subgrade displacement sequence is used as the predicted displacement sequence. The forward prediction model is inverted based on the predicted displacement sequence to obtain the dynamic inversion model of subgrade soil parameters. S6: Based on the dynamic inversion model of subgrade soil parameters, construct a comprehensive weighted displacement index, and establish a comprehensive performance evaluation index and hierarchical early warning system for subgrade based on the comprehensive weighted displacement index, and output the subgrade status identification results.
2. The railway subgrade performance evaluation method based on dynamic proxy analysis according to claim 1, characterized in that, S2 includes: S21: Determine the time-varying parameters of soil mechanics and their value ranges; the time-varying parameters of soil mechanics include the elastic modulus and Poisson's ratio; S22: Sampling of time-varying soil mechanics parameters within the parameter value range to obtain multiple parameter combinations; S23: Construct a finite element model of the roadbed; the finite element model of the roadbed is used to simulate the long-term deformation process of the roadbed soil. S24: Input each set of parameters into the roadbed finite element model in sequence, perform dynamic simulation calculation, and obtain the finite element dynamic simulation results.
3. The railway subgrade performance evaluation method based on dynamic proxy analysis according to claim 2, characterized in that, The range of values for the elastic modulus and Poisson's ratio is as follows: ； ； in, and These are the elastic modulus and Poisson's ratio of the l-th soil layer at the initial moment of the analysis, respectively. and These are the minimum and maximum elastic moduli of the l-th soil layer at the initial time, respectively; and These are the minimum and maximum Poisson's ratios of the l-th soil layer at the initial time, respectively. For the number of soil layers, ; This refers to the number of soil layers in the roadbed. Multiple parameter combinations are as follows: ； ； ； in, and These are the initial elastic modulus vector and initial Poisson's ratio vector of each soil layer in the nth group of parameters, respectively. and These are the elastic modulus and Poisson's ratio of the first soil layer of the nth model at the initial moment, obtained by the Latin hypercube sampling method. and These are the elastic modulus and Poisson's ratio of the second soil layer in the nth model at the initial moment, obtained by the Latin hypercube sampling method. and , respectively, represent the elastic modulus and Poisson's ratio of the Lth soil layer in the nth model at the initial moment, obtained by the Latin hypercube sampling method; n is the variable of the subgrade finite element model. N represents the total number of finite element models of the roadbed.
4. The railway subgrade performance evaluation method based on dynamic proxy analysis according to claim 1, characterized in that, The S3 includes: S31: Collect the time-varying parameters of soil mechanics and the displacement values of the subgrade from the finite element dynamic simulation results, and construct training samples; S32: Divide the training samples to obtain the training set and the test set.
5. The railway subgrade performance evaluation method based on dynamic proxy analysis according to claim 1, characterized in that, The S4 includes: S41: Construct a spatiotemporal sequence dynamic proxy model; the input of the spatiotemporal sequence dynamic proxy model is a time series data pair, and the output is the roadbed displacement value; S42: Train the spatiotemporal sequence dynamic surrogate model using the training set in the training samples to obtain the trained spatiotemporal sequence dynamic surrogate model; S43: Test the trained spatiotemporal sequence dynamic surrogate model using the test set in the training samples to obtain the model performance, and optimize the trained spatiotemporal sequence dynamic surrogate model to obtain the final spatiotemporal sequence dynamic surrogate model.
6. The railway subgrade performance evaluation method based on dynamic proxy analysis according to claim 5, characterized in that, The loss function for training the spatiotemporal sequence dynamic surrogate model is: ； ； ； ； ； in, The loss function used to train the spatiotemporal sequence dynamic surrogate model; This is the tradeoff coefficient between data fitting loss and physical constraint loss; The mean square error between the model's predicted values and the actual values from the finite element dynamic simulation. , and These are the weight coefficients for the mechanical consistency constraint, the time smoothness constraint, and the monotonicity constraint, respectively. For mechanical consistency constraints; For time-series smoothing constraints; This is a monotonicity constraint term; The number of samples in the training set is T; the time step length is n; and the variables in the roadbed finite element model are n. and These are the displacement values predicted by the dynamic surrogate model for the nth model at times t-1 and t, respectively; The displacement value is obtained from the finite element dynamic simulation calculation of the nth model at time t; t is the time variable. The number of soil layers is a variable; This refers to the number of soil layers in the roadbed. This represents the elastic modulus matrix of the l-th subgrade soil extracted by the nth model at time t. The Poisson's ratio matrix of the l-th subgrade soil extracted by the n-th model at time t; The optimization constraints for the spatiotemporal sequence dynamic surrogate model are as follows: ； in, This represents the number of CNN convolutional kernels. and The number of CNN convolution kernels The minimum and maximum values can be obtained; This represents the number of hidden units in the GRU. and These represent the number of hidden units in the GRU. The minimum and maximum values can be obtained; The learning rate; For learning rate The maximum value; The optimized function is: ； in, To optimize the function; is the number of samples in the test set; n is the variable in the roadbed finite element model.
7. The railway subgrade performance evaluation method based on dynamic surrogate analysis according to claim 1, characterized in that, The S5 includes: S51: The final spatiotemporal sequence dynamic proxy model is used as the forward prediction model, and the subgrade displacement sequence is used as the predicted displacement sequence of the forward prediction model. The inversion elastic modulus and inversion Poisson's ratio of each layer of subgrade soil are obtained through inversion. S52: Based on the inverted elastic modulus and inverted Poisson's ratio, construct a dynamic inversion model of subgrade soil parameters; S53: Based on the roadbed displacement sequence, inverted elastic modulus and inverted Poisson's ratio, the dynamic inversion model of roadbed soil parameters is updated to obtain the parameter state vector of the soil. S54: Based on the soil parameter state vector, the dynamic inversion model of subgrade soil parameters is optimized to obtain the final dynamic inversion model of subgrade soil parameters.
8. The railway subgrade performance evaluation method based on dynamic proxy analysis according to claim 7, characterized in that, The dynamic inversion model for subgrade soil parameters is as follows: ； ； in, In order to be in The elastic modulus vector obtained by inversion at time step; In order to be in The Poisson's ratio vector obtained by time-inversion; and The l-th soil layer is located at... The elastic modulus and Poisson's ratio obtained by inversion at each moment ; For the number of soil layers, This refers to the number of soil layers in the roadbed. The updated dynamic inversion model for subgrade soil parameters is as follows: ； ； in, Let h be the parameter state vector of the soil in the k-th set at time h; The predicted state vector of the soil in the k-th set at time h before updating the dynamic inversion model of subgrade soil parameters; This represents the actual monitored displacement in the roadbed displacement sequence; The displacement is the forward prediction obtained by the surrogate model for the k-th set; Kalman gain; This is the forward mapping function of the trained CNN-GRU spatiotemporal sequence dynamic surrogate model; The optimized dynamic inversion model for subgrade soil parameters is as follows: ； ； ； ； in, To optimize the dynamic inversion model of subgrade soil parameters; These are the weighting coefficients for the prediction error term, the parameter prior constraint term, and the parameter stability constraint term, respectively. The root mean square error is the average error of the entire sample. For the prior deviation of the parameter; is the parameter stability index; h is the time variable; H is the monitoring duration; k is the indicator variable; K is the total number of indicators; Let h be the parameter state vector of the soil in the k-th set at time h; This is the transpose of the matrix; The second norm of a vector; This is the weight matrix; Let be the parameter state vector of the soil in the k-th set at time h-1.
9. The railway subgrade performance evaluation method based on dynamic proxy analysis according to claim 1, characterized in that, The S6 includes: S61: Based on the dynamic inversion model of subgrade soil parameters, calculate the overall equivalent elastic modulus and overall equivalent Poisson's ratio of the subgrade soil. S62: Based on the overall equivalent elastic modulus and the overall equivalent Poisson's ratio, construct the comprehensive weighted displacement index of the roadbed; S63: Based on the comprehensive weighted displacement index and the standard limit of subgrade displacement, a hierarchical early warning system is established to obtain the subgrade condition identification results.
10. The railway subgrade performance evaluation method based on dynamic proxy analysis according to claim 9, characterized in that, The overall equivalent elastic modulus and the overall equivalent Poisson's ratio are: ； ； in, and These are the overall equivalent elastic modulus and the overall equivalent Poisson's ratio, respectively. For the number of soil layers, This refers to the number of soil layers in the roadbed. The thickness of the l-th soil layer; and These are the elastic modulus and Poisson's ratio of the l-th soil layer at time h, respectively. The comprehensive weighted displacement index is: ； in, For comprehensive weighted displacement index; and These are the overall equivalent elastic modulus and the overall equivalent Poisson's ratio under the initial state of the roadbed, respectively. The monitored displacement of the roadbed at time h; The roadbed displacement limit was determined according to engineering specifications; , and The weighting coefficients for the first, second, and third entropy values are as follows: ； ； ； ； in, A standardized vector; This represents the percentage of the k-th indicator. Let h be the standardized value of the k-th index at time h; h is a time variable; Let ln be the information entropy of the k-th index; ln is the logarithmic function. The entropy value weight of the k-th indicator; For monitoring duration.