Method and system for determining limit value of uneven settlement of high-speed railway subgrade based on physical constraint active learning agent model

Abstract

The present application relates to a kind of high-speed railway subgrade uneven settlement limit value determination method and system based on physical constraint active learning agent model.The method obtains train, track, subgrade and foundation parameters, establishes vehicle-track-settlement subgrade coupling finite element model, and with it as high fidelity sample generator;Settlement form, structure parameters and speed working condition joint coding are constructed, and high fidelity sample library is generated;Train data fitting term, settlement risk monotonicity constraint, physical boundary constraint and threshold boundary constraint are contained in agent model, and multiple indexes such as vehicle safety, ride comfort, track structure response and subgrade dynamic response are predicted;Based on the uncertainty of prediction, threshold boundary proximity and parameter space coverage active supplement finite element sample;Under the constraint of multiple index threshold, the minimum critical settlement amplitude is back calculated, and settlement limit value curve, limit value surface and risk grade are output.The method can reduce repeated finite element calculation, improve critical boundary prediction accuracy and physical consistency.

Description

Technical Field

[0001] This invention relates to the fields of computer-aided analysis of high-speed railway engineering, coupled dynamic simulation of vehicle-track-subgrade, machine learning surrogate models, and control of uneven subgrade settlement. In particular, it relates to a method and system for determining the limit of uneven settlement of high-speed railway subgrade based on a coupled finite element high-fidelity sample library and a physical constraint active learning surrogate model. Background Technology

[0002] High-speed railways place high demands on track structure smoothness, subgrade foundation stability, and vehicle operation safety. The subgrade may experience uneven settlement under the influence of factors such as train cyclic loads, self-weight loads, foundation consolidation, disturbance from construction of adjacent new lines, underground excavation, and changes in the groundwater environment. Uneven subgrade settlement can cause additional deformation of the track structure, alter the wheel-rail contact state, increase wheel-rail dynamics, and potentially affect train operation safety, passenger comfort, and the performance of ballastless track structures.

[0003] Existing technologies are capable of calculating the dynamic response of high-speed railways using coupled finite element models of vehicles, tracks, and subgrades or vehicles, tracks, and foundations. For example, some schemes focus on establishing coupled modeling methods for high-speed railway subgrades that consider wheel-rail rolling contact; others determine the limits of uneven subgrade settlement by establishing coupled finite element models of the high-speed railway system and comparing them with standard thresholds; still others improve the efficiency of track structure parameter optimization, route scheme evaluation, or reliability analysis through surrogate models or multi-objective optimization.

[0004] However, existing methods still have shortcomings. First, settlement limits are influenced by multiple factors, including settlement amplitude, settlement wavelength, settlement location, settlement type, train speed, vehicle type, fastener stiffness, track slab parameters, support layer parameters, subgrade modulus, and foundation modulus. Performing high-fidelity finite element calculations for each parameter combination would result in a large amount of redundant calculations. Second, traditional working condition selection often relies on manual experience, making it difficult to guarantee sufficient samples near the critical settlement limit boundary. Third, ordinary surrogate models mainly rely on data fitting, which may lead to prediction results that do not conform to engineering principles, such as a decrease in risk assessment value when settlement amplitude increases, or wheel-rail force or stress exceeding physical boundaries. Fourth, the area near the critical settlement boundary is highly sensitive to prediction errors; even surrogate models with small overall errors may still give conservative or unsafe limits near the threshold. Fifth, a single evaluation index cannot fully reflect the comprehensive risks of vehicle safety, ride comfort, track structure dynamic response, and subgrade dynamic response.

[0005] Therefore, a new technical solution is needed that, while retaining the high-fidelity analysis capability of the vehicle-track-settlement subgrade coupled finite element model, improves the multi-condition prediction efficiency through a physical constraint proxy model, and automatically supplements finite element samples near high uncertainty and threshold boundaries through active learning, thereby quickly, stably and reliably determining the non-uniform settlement limit of high-speed railway subgrade. Summary of the Invention

[0006] The purpose of this invention is to provide a method and system for determining the non-uniform settlement limit of high-speed railway subgrade based on a physical constraint active learning surrogate model, so as to solve the problems of large computational load of multi-condition finite element method, dependence on manual experience in condition selection, lack of physical consistency of ordinary surrogate models, insufficient samples near the threshold boundary, and difficulty in quickly outputting continuous settlement limit curves or limit surfaces in the existing technology.

[0007] The technical solution of the present invention is as follows: A method for determining the limit of uneven settlement of high-speed railway subgrade based on a physical constraint active learning surrogate model is characterized by the following steps: S1: Obtain high-speed railway engineering design information, train operation parameters, track structure parameters, roadbed structure parameters and foundation parameters, and establish a vehicle-track-settlement roadbed coupled finite element model based on the parameters.

[0008] Preferably, the engineering design information may include the line grade, track structure type, roadbed cross-section type, support layer structure type, subgrade structure type, and foundation treatment type; train operation parameters may include train type, operating speed, axle load, wheelset spacing, and formation; track structure parameters may include rail type, fastener stiffness, fastener damping, track slab elastic modulus, ballast slab elastic modulus, and support layer elastic modulus; roadbed and foundation parameters may include the elastic modulus, density, Poisson's ratio, and damping parameters of the subgrade surface layer, subgrade bottom layer, roadbed body, and foundation.

[0009] Preferably, the vehicle-track-settlement subgrade coupled finite element model includes a high-speed train system, a ballastless track system, and a settlement subgrade system. The high-speed train system consists of a car body, bogies, and wheelsets, with the car body and bogies, and the bogies and wheelsets, connected by primary and secondary suspension systems. The ballastless track system includes rails, fasteners, sleepers or track slabs, ballast slabs, and a support layer. The settlement subgrade system includes a subgrade surface layer, a subgrade bottom layer, the subgrade body, and the foundation. The settlement morphology can be formed by modifying node coordinates, importing settlement curves, setting an initial displacement field, geometric cutting, or regenerating the settlement subgrade geometric model.

[0010] S2: Construct a multi-condition parameter space, which includes settlement morphology parameters, structural parameters, and velocity condition parameters, and encode the settlement morphology parameters, structural parameters, and velocity condition parameters into settlement morphology codes, structural parameter codes, and velocity condition codes, respectively.

[0011] Preferably, the settlement morphology parameters include settlement type, settlement amplitude, settlement wavelength, settlement center location, settlement start and end locations, settlement influence range, maximum settlement slope, and maximum settlement curvature. Settlement types include misaligned settlement, cosine settlement, Gaussian trough settlement, bridge-road transition section settlement, tunnel-road transition section settlement, and localized abrupt settlement. Structural parameters include fastener stiffness, fastener damping, track slab elastic modulus, subgrade surface elastic modulus, subgrade bottom elastic modulus, roadbed body elastic modulus, and foundation elastic modulus. Speed-related parameters include train speed, vehicle type, and axle load.

[0012] In the feature encoding step, the settlement morphology encoding, structural parameter encoding, and velocity condition encoding are combined into the input features of the surrogate model: X =[ X s , X p , X v ].in, X This is the input feature vector for the physical constraint surrogate model; X s Encoding the settlement morphology is used to characterize settlement morphology parameters; X p Structural parameters are encoded to characterize the structural parameters of the track, roadbed, and foundation. X v The speed condition code is used to characterize speed condition parameters such as train operating speed, vehicle type, and axle load; square brackets indicate that the above three types of codes are combined into the same input feature vector.

[0013] For complex settlement curves, the settlement curve can be discretized along the track direction as follows: S =[ s 1, s 2, ..., s n This, along with settlement type, amplitude, wavelength, slope, and curvature, forms the settlement morphology code. S This is the discrete vector of the settlement curve formed after discrete sampling of the settlement curve along the line direction; s 1, s 2, ..., s n These represent the settlement displacements at each sampling point, arranged in the sampling order along the route. nThe total number of sampling points is represented by the same unit of length for each settlement displacement.

[0014] S3: Generate an initial working condition sample set based on the multi-working condition parameter space, call the vehicle-track-settlement subgrade coupled finite element model to perform dynamic calculations on the initial working condition sample set, extract multiple dynamic evaluation indicators, and form a high-fidelity sample library.

[0015] Preferably, an initial set of working condition samples is generated using orthogonal experiments, Latin hypercube sampling, uniform design, Sobol sequence sampling, or random sampling. For each working condition sample, the settlement morphology, structural parameters, and velocity conditions in the finite element model are automatically modified, finite element dynamic calculations are run, and multiple dynamic evaluation indices are extracted. These multiple dynamic evaluation indices include vehicle safety indices, ride comfort indices, track structure dynamic response indices, and roadbed dynamic response indices.

[0016] S4: Train a physical constraint proxy model based on the high-fidelity sample library. The physical constraint proxy model takes the settlement morphology code, structural parameter code, and velocity condition code as input and the multi-dynamic evaluation index as output. The training loss function includes a data fitting term and a physical constraint term.

[0017] Preferably, the surrogate model can be Gaussian process regression, random forest, gradient boosting tree, support vector regression, deep neural network, graph neural network, physically constrained neural network, or ensemble learning model.

[0018] The training loss function is: L=L data +λ 1 L mono +λ 2 L bound +λ 3 L limit In the formula, L This represents the total loss during training of the physical constraint surrogate model. l 1. l 2. l 3 represents the monotonic constraint loss L of settlement risk. mono Physical boundary constraint loss L bound And evaluation index threshold boundary constraint loss L limit The weighting coefficients are used to adjust the relative contributions of the three constraint loss terms to the total loss.

[0019] Among them, data fitting loss L dataUsed to constrain the error between the surrogate model's predicted values ​​and the high-fidelity finite element sample values; settlement risk monotonicity constraint loss L mono Used to ensure that, under the same structural parameters and speed conditions, the settlement risk assessment value does not decrease within a preset allowable error range as the settlement amplitude, settlement slope, or settlement curvature increases; physical boundary constraint loss L bound Preset physical boundaries are used to constrain the output of the surrogate model to meet the requirements of wheel-rail force, derailment coefficient, wheel load reduction rate, structural displacement, acceleration, and stress; threshold boundary constraint loss L limit Used to enhance the predictive consistency of the surrogate model near the evaluation metric threshold.

[0020] S5: Construct a set of candidate working conditions, use the physical constraint surrogate model to predict the multi-dynamic evaluation indexes and prediction uncertainties corresponding to the candidate working conditions, and determine supplementary working conditions based on the prediction uncertainty, the degree to which the candidate working conditions approach the threshold boundary of the evaluation indexes, and the contribution of the candidate working conditions to the parameter space coverage.

[0021] In the active learning supplementation step, an active learning sampling function is constructed: A ( x )= αU ( x )+ βB ( x )+ γC ( x ).in, x The candidate working condition is represented by an input feature vector consisting of the settlement morphology code, structural parameter code, and velocity working condition code corresponding to the candidate working condition. A ( x ) is the candidate operating condition x Comprehensive sampling indicators; U ( x ) is the surrogate model prediction uncertainty index for candidate working condition x; B ( x ) is the candidate operating condition x The threshold boundary proximity index is used to characterize the degree to which its prediction result approaches the threshold boundary of any dynamic evaluation index. C ( x ) is the candidate operating condition x The parameter space coverage index is used to characterize its supplementary contribution to the parameter space coverage of existing high-fidelity samples. α , β , c These are the weighting coefficients for the prediction uncertainty index, the threshold boundary proximity index, and the parameter space coverage index, respectively.

[0022] Preferably, the prediction uncertainty is obtained by statistical analysis of multiple prediction results of the physical constraint surrogate model, including: for a Gaussian process regression model, obtaining the prediction uncertainty from its posterior variance; for an ensemble learning model, obtaining the prediction uncertainty from the standard deviation between the prediction results of each sub-model; and for a deep neural network model, obtaining the prediction uncertainty from the variance of the prediction results under multiple random deactivation conditions using the MC Dropout method.

[0023] Preferably, the supplementary working condition is determined as follows: for each candidate working condition in the candidate working condition set, its prediction uncertainty index, threshold boundary proximity index, and parameter space coverage index are calculated respectively. The three indices are weighted and combined to obtain a comprehensive sampling index. The candidate working conditions are sorted in descending order of the comprehensive sampling index, and the candidate working condition with the highest ranking is selected as the supplementary working condition. The higher the comprehensive sampling index value, the more valuable the candidate working condition is for improving the prediction accuracy of the surrogate model near the settlement limit critical boundary.

[0024] More preferably, the threshold boundary proximity index is used to measure the degree to which the surrogate model prediction value of the candidate working condition is close to the threshold boundary of any dynamic evaluation index. Its value is obtained by calculating the difference between the prediction value of each evaluation index and its corresponding threshold and taking the reciprocal. The smaller the difference, the higher the threshold boundary proximity index. This index makes working conditions close to the critical boundary preferred as supplementary working conditions. The parameter space coverage index is used to measure the supplementary contribution of the candidate working condition to the parameter space coverage of the existing high-fidelity samples. Its value is obtained by calculating the minimum distance or kernel density estimation between the candidate working condition and the existing high-fidelity samples in the input feature space. The farther the candidate working condition is from the existing samples, the higher the parameter space coverage index. This index makes working conditions in the sparse sample region of the parameter space preferred as supplementary working conditions.

[0025] S6: Call the vehicle-track-settlement subgrade coupled finite element model to perform dynamic calculations on the supplementary working condition, add the calculation results to the high-fidelity sample library, and update the physical constraint proxy model.

[0026] S7: Repeat the above-mentioned candidate working condition prediction, supplementary working condition selection, finite element sampling calculation and surrogate model update until the preset convergence condition is met.

[0027] Preferably, the preset convergence condition includes at least one of the following conditions: the maximum prediction uncertainty of the surrogate model on the candidate working condition set is lower than a preset uncertainty threshold; the relative change rate of the settlement limit obtained by two consecutive iterations is lower than a preset change rate threshold; the cumulative number of supplementary working conditions reaches a preset upper limit; the prediction error of the surrogate model on the verification sample is lower than a preset error threshold; when any of the above conditions are met, the iteration stops, and the current surrogate model is used as the final prediction model for the settlement limit inversion.

[0028] S8: Using the updated physical constraint proxy model, under given train speed, structural parameters and settlement morphology, the minimum critical settlement amplitude that meets the threshold requirements of multiple dynamic evaluation indicators is inversely calculated, and the minimum critical settlement amplitude is determined as the subgrade uneven settlement limit.

[0029] Preferably, the specific implementation of the reverse calculation of the minimum critical settlement amplitude that satisfies the threshold requirements of multiple dynamic evaluation indicators is as follows: for each dynamic evaluation indicator, within a preset settlement amplitude range, the critical settlement amplitude when the indicator reaches the corresponding threshold is solved by a computer-executed binary search, monotonic interpolation, or constrained optimization algorithm. The minimum value among the critical settlement amplitudes corresponding to each indicator is taken as the roadbed uneven settlement limit controlled by the most unfavorable evaluation indicator, and the evaluation indicator corresponding to the minimum value is identified as the control indicator.

[0030] For each evaluation index, determine the critical settlement amplitude at which it reaches the threshold, and take the minimum value as the limit for uneven settlement of the roadbed: d lim = minutes ( d 1, d 2, ..., d m ).in, d lim The subscript "lim" represents the limit value for uneven settlement of the roadbed, determined under given train speed, structural parameters, and settlement morphology. d 1, d 2, ..., d m These are the critical settlement amplitude values ​​when each dynamic evaluation index reaches its corresponding threshold. m This represents the total number of dynamic evaluation indicators used in the reverse calculation of settlement limits; min indicates the minimum value operation, and all critical settlement amplitudes use the same length unit.

[0031] Preferably, the uneven settlement limit of the roadbed is output through a computer graphical interface or data interface in the form of a settlement limit curve, a settlement limit surface, or a risk level; the settlement limit curve is plotted with train speed or settlement wavelength as the abscissa and the maximum allowable settlement amplitude as the ordinate, to characterize the maximum allowable settlement amplitude under different train speeds, different settlement wavelengths, or different settlement types; the settlement limit surface is constructed as a three-dimensional surface with train speed and settlement wavelength as two dimensions and the maximum allowable settlement amplitude as the third dimension, to characterize the correspondence between train speed, settlement wavelength, and the maximum allowable settlement amplitude; the risk level is determined based on the maximum value of the ratio between the predicted value of each evaluation index and its corresponding threshold, and is used for graded early warning of actual settlement conditions.

[0032] More preferably, the risk level is determined through the following computer-executed evaluation process: based on the predicted values ​​of each dynamic evaluation index output by the surrogate model, the ratio of the predicted value of each evaluation index to its corresponding threshold is calculated one by one, and the maximum value is taken as the settlement risk evaluation value. The corresponding risk level identifier is output according to the preset risk level range into which the settlement risk evaluation value falls. The preset risk level range includes a low-risk range, a concern range, a warning range, and an over-limit range, which correspond to different levels of engineering response measures.

[0033] To implement the above method, this invention also provides a system for determining the non-uniform settlement limit of high-speed railway subgrade based on a physical constraint active learning surrogate model, comprising: The model building module is used to acquire high-speed railway engineering design information, train operation parameters, track structure parameters, roadbed structure parameters and foundation parameters, and to establish a vehicle-track-settlement roadbed coupled finite element model; The sample generation module is used to construct a multi-condition parameter space including settlement morphology parameters, structural parameters and velocity condition parameters, generate an initial condition sample set, call the vehicle-track-settlement subgrade coupled finite element model for dynamic calculation, and form a high-fidelity sample library. The surrogate model training module is used to train a physical constraint surrogate model that includes data fitting terms and physical constraint terms by taking the settlement morphology code, structural parameter code and velocity condition code as numerical input features and multiple dynamic evaluation indicators as output. The active learning supplementary sampling module is used to determine supplementary working conditions based on the surrogate model's prediction uncertainty, threshold boundary proximity, and parameter space coverage. It calls the vehicle-track-settlement subgrade coupled finite element model to perform supplementary sampling calculations and update the surrogate model. The limit inverse calculation module is used to inversely calculate the minimum critical settlement amplitude that meets the threshold requirements of multiple dynamic evaluation indicators under given train running speed, structural parameters and settlement morphology conditions. The results output module is used to output the settlement limit curve, settlement limit surface, and risk level.

[0034] Preferably, the active learning supplementation module includes: an uncertainty evaluation unit for calculating the surrogate model prediction uncertainty of candidate working conditions; a threshold boundary proximity evaluation unit for calculating the degree to which candidate working conditions approach the threshold boundaries of each evaluation index; a parameter space coverage evaluation unit for calculating the supplementary contribution of candidate working conditions to the parameter space coverage of existing high-fidelity samples; a comprehensive sampling index calculation unit for weighted summarization of the prediction uncertainty, threshold boundary proximity, and parameter space coverage to obtain the comprehensive sampling index of each candidate working condition; a working condition sorting and selection unit for sorting candidate working conditions from largest to smallest according to the comprehensive sampling index and selecting supplementary working conditions; and a finite element supplementation scheduling unit for automatically modifying the input parameters of the vehicle-track-settlement subgrade coupled finite element model, submitting finite element calculation tasks, and extracting calculation results.

[0035] Preferably, the result output module is also used to output the number of resampling rounds, the surrogate model error change curve, the identification results of the control evaluation index, and the settlement limit convergence process; the control evaluation index is the evaluation index corresponding to the minimum value among the critical settlement amplitudes corresponding to each dynamic evaluation index, and the settlement limit convergence process is plotted with the number of iteration rounds as the horizontal axis and the settlement limit obtained by inversion as the vertical axis, which is used to show the stable process of the settlement limit with active learning resampling iteration.

[0036] Compared with the prior art, the present invention has the following advantages: (1) Reduce redundant finite element calculations. This invention generates high-fidelity samples using a vehicle-track-settlement subgrade coupled finite element model, and then uses a proxy model to perform rapid predictions for multiple working conditions, which can significantly reduce the number of redundant finite element calculations.

[0037] (2) Improve the efficiency of settlement limit determination. After training, the surrogate model can quickly predict multiple dynamic evaluation indicators, so that the settlement limit curve and limit surface can be generated in a short time.

[0038] (3) Improve prediction accuracy near the threshold. The active learning sampling function focuses the supplementation on working conditions with high prediction uncertainty, close to the threshold boundary of the evaluation index, and contributing to the coverage of the parameter space, thereby improving the prediction accuracy near the critical settlement boundary.

[0039] (4) Ensure that the prediction results conform to physical laws. Monotonicity constraints, physical boundary constraints, and threshold boundary constraints of evaluation indicators for settlement risk can reduce non-physical predictions of ordinary surrogate models.

[0040] (5) Simultaneously consider vehicle safety, ride comfort, track structure response, and subgrade dynamic response. The final limit is controlled by the most unfavorable critical settlement amplitude among multiple indicators, which better reflects the comprehensive risk of the vehicle-track-subgrade system.

[0041] (6) It can output settlement limit curves, limit surfaces and risk levels under different speeds, settlement wavelengths, settlement types and structural parameters, providing a basis for high-speed railway subgrade settlement control, operation and maintenance and speed limit decision-making. Attached Figure Description

[0042] Figure 1 This is an overall flowchart of the method of the present invention.

[0043] Figure 2 This is a schematic diagram of a coupled finite element model of vehicle-track-settlement subgrade.

[0044] In the diagram, 1 is the car body, 2 is the secondary suspension, 3 is the bogie, 4 is the primary suspension, 5 is the wheelset, 6 is the rail, 7 is the fastener, 8 is the double-block sleeper, 9 is the track bed slab, 10 is the support layer, and 11 is the roadbed.

[0045] Figure 3 This is a schematic diagram of the wheel-rail contact model used in this invention.

[0046] Figure 4 This is a structural diagram of the physical constraint proxy model of the present invention.

[0047] Figure 5 This is a flowchart of the active learning and replenishment process of this invention; Figure 6 This is a schematic diagram illustrating the reverse calculation of settlement limits and the output of risk levels in this invention. Detailed Implementation

[0048] The present invention will be described below with reference to a specific engineering process. This embodiment is for illustrative purposes only and does not constitute a limitation on the scope of protection. In actual engineering, parameters can be replaced according to the specific route, vehicle type, track structure, roadbed cross-section, and foundation conditions.

[0049] Step 1, Input Parameters. Input engineering design information, train speed, vehicle axle load, wheelset spacing, rail type, fastener stiffness and damping, track slab elastic modulus, support layer elastic modulus, subgrade surface elastic modulus, subgrade bottom layer elastic modulus, roadbed body elastic modulus, foundation elastic modulus, damping parameters, and track irregularity level.

[0050] Step 2: Establish a coupled finite element model of the vehicle-track-settlement subgrade. The vehicle system can be modeled using a multi-rigid-body approach, while the track and subgrade systems can be modeled using solid elements or equivalent elements. Wheel-rail normal contact can be modeled using Hertz nonlinear contact or contact pressure-interference relationship, while wheel-rail tangential contact can be modeled using a penalty function friction model or creep model. Fasteners and suspension systems use spring-damped or connecting elements. Damped boundaries or infinite element boundaries are used for the boundaries to reduce dynamic wave reflection.

[0051] Step 3: Settlement morphology parameterization. For cosine-type settlement, Gaussian trough-type settlement, and stepped settlement, parameterization is performed using settlement amplitude, settlement wavelength, settlement center location, settlement slope, and settlement curvature, respectively. The aforementioned settlement curves can also be discretized into several sampling points as model input.

[0052] Step 4: Generate high-fidelity samples. Initial samples are generated using Latin hypercube sampling. Each sample includes settlement type, settlement amplitude, settlement wavelength, settlement location, structural parameters, and velocity conditions. The finite element model is automatically modified via script, the calculation task is submitted, and indicators such as wheel-rail vertical force, wheel-rail lateral force, derailment coefficient, wheel load reduction rate, vehicle acceleration, rail displacement, track slab stress, and subgrade dynamic stress are extracted.

[0053] Step 5: Train the physical constraint surrogate model. Standardize the input features and input them into the surrogate model. For neural network models, a multi-task output structure can be used; for ensemble models, multiple sub-models can be trained and their mean taken as the prediction result, with the prediction variance taken as the uncertainty. During training, data fitting terms, settlement risk monotonicity constraints, physical boundary constraints, and threshold boundary constraints are included.

[0054] Step 6, Active Learning Supplementation. Construct a candidate working condition set and calculate the active learning sampling function. The threshold boundary proximity can be taken as the reciprocal of the distance between the candidate working condition and the threshold of each index; the closer the candidate working condition is to any threshold boundary, the greater the threshold boundary proximity. Spatial coverage can be represented by the minimum distance or kernel density between the candidate sample and the selected sample. Select the top-ranked candidate working conditions to supplement the finite element calculation.

[0055] Step 7, Convergence Judgment. If the rate of change of settlement limit values ​​for two consecutive rounds is less than a preset threshold, or the MAPE of the validation samples near the threshold is less than a preset error, or the uncertainty of the surrogate model prediction is lower than a preset threshold, then sampling is stopped. Here, MAPE is the mean absolute percentage error, used to characterize the average relative error magnitude of the surrogate model prediction value relative to the calculated value of the high-fidelity samples.

[0056] Step 8, Limit Inverse Calculation. For a given velocity, structural parameters, and settlement type, within the settlement amplitude range, use a binary search or monotonic interpolation to find the critical settlement amplitude at which each evaluation index reaches the threshold. Take the minimum value as the final settlement limit and output the limit curve, limit surface, and risk level.

[0057] The cosine-type settlement curve can be represented as: s ( x )= d [1- cos (2 π ( x - x 0) / L )] / 2. Among them, s ( x The coordinates along the route are... x Settlement displacement at the location; x These are the position coordinates along the route; d This represents the settlement amplitude. x 0 represents the phase reference coordinates for determining the position of the cosine-type settlement curve along the line; L The settling wavelength in this formula; π Pi; cos represents the cosine function. x , x 0 and L Using the same unit of length, s ( x )and d Use the same unit of length.

[0058] The Gaussian trough settlement curve can be expressed as: s ( x )= exp [-( x - x 0) 2 / (2 b 2 )].in, s ( x The coordinates along the route are... x Settlement displacement at the location; x These are the position coordinates along the route; d This represents the maximum settlement amplitude of the Gaussian trough-shaped settlement. x 0 represents the coordinate of the center of the Gaussian settling trough along the line in this formula; b Dimensional parameters for controlling the width of the Gaussian settling trough; exp This represents the natural exponential function. x , x 0 and b Using the same unit of length, s ( x )and d Use the same unit of length.

[0059] Example 1: Determination of Uneven Settlement Limits for High-Speed ​​Railway Subgrade Based on Exemplary Simulation Data The following data are exemplary simulation data used to illustrate the method of the present invention, and are not actual field measurement data. In actual engineering, they can be replaced according to the specific route, vehicle and foundation parameters.

[0060] (I) Implementation Scenarios and Input Parameters This embodiment is set as a ballastless track high-speed railway. Train speeds are 250 km / h, 300 km / h, 350 km / h, and 400 km / h; settlement types are cosine settlement, Gaussian trough settlement, and misaligned settlement; settlement amplitudes are 2 mm, 4 mm, 6 mm, 8 mm, 10 mm, and 12 mm; and settlement wavelengths are 20 m, 40 m, and 60 m. Evaluation indicators include wheel-rail vertical force, wheel-rail lateral force, derailment coefficient, wheel load reduction rate, car body vertical acceleration, rail vertical displacement, track slab stress, and subgrade dynamic stress.

[0061] Table 1 Input parameters for the example (II) High-fidelity sample library and active learning supplementation Initially, 180 samples were generated using Latin hypercube sampling. For each sample, a coupled finite element model of the vehicle-track-settlement subgrade was used for dynamic calculations. After the initial surrogate model was trained, a candidate set of working conditions was constructed, and supplementary working conditions were selected using an active learning sampling function. In each round of supplementation, working conditions with higher prediction uncertainty and close to the threshold boundary were prioritized.

[0062] Active learning sampling function is A ( x )= αU ( x )+ βB ( x )+ γC ( x ).in, x This represents a candidate working condition in the candidate working condition set of this embodiment, represented by its corresponding input feature vector; A ( x ) is the candidate operating condition x Comprehensive sampling indicators; U ( x ) is the candidate operating condition x The proxy model predicts uncertainty indicators; B ( x ) is the candidate operating condition x Threshold boundary proximity index;C ( x ) is the candidate operating condition x The parameter space coverage index; α , β , c These are the weighting coefficients for the aforementioned prediction uncertainty index, threshold boundary proximity index, and parameter space coverage index. The symbols above have the same meaning as the corresponding symbols in the aforementioned active learning supplementation step.

[0063] Table 2. Active Learning Compensation and Surrogate Model Errors (III) Risk assessment under different settlement amplitudes Under the example conditions of train speed of 350 km / h, settlement wavelength of 40 m, and cosine-type settlement, each evaluation index is divided by its corresponding threshold to obtain a normalized value, and the maximum normalized value is taken as the risk assessment value. The settlement risk assessment value does not decrease with the increase of settlement amplitude, which meets the monotonicity constraint of settlement risk.

[0064] Risk assessment value is defined as R = max ( I 1 / I 1,lim , I 2 / I 2,lim , ..., I m / I m,lim ).in, R The value is the settlement risk assessment value, which is a dimensionless quantity. I 1. I 2, ... I m These are the values ​​of each dynamic evaluation index involved in the risk assessment; I 1,lim , I 2,lim ... I m,lim These are the threshold values ​​corresponding to the aforementioned kinetic evaluation indicators, with the subscript "lim" indicating the threshold value of the corresponding indicator; m is the total number of kinetic evaluation indicators participating in the risk assessment; the ratio of each kinetic evaluation indicator value to its corresponding threshold value is the normalized value of that evaluation indicator, and both are calculated using the same unit; max indicates the operation of taking the maximum value.

[0065] Table 3 Risk assessment values ​​under different settlement amplitudes (iv) Settlement limits at different velocities and settlement wavelengths An updated physical constraint surrogate model is used to search for the critical settlement amplitude at which each evaluation index reaches its threshold under each combination of velocity and settlement wavelength, and the minimum value among them is taken as the allowable settlement limit. Example results show that the higher the velocity, the smaller the allowable settlement limit is generally; the longer the settlement wavelength, the relatively larger the allowable settlement limit is at the same velocity.

[0066] Table 4 Settlement limits obtained by reverse calculation under different velocities and settlement wavelengths (v) Critical Settlement Amplitude of Multiple Indicators Taking a speed of 350 km / h, cosine-type settlement, and a settlement wavelength of 40 m as an example, the critical settlement amplitude was calculated for each dynamic evaluation index. The results show that the critical settlement amplitude is smallest when the vehicle body vertical acceleration reaches the threshold. Therefore, the final settlement limit is controlled by the vehicle body vertical acceleration.

[0067] Table 5 Comparison of Critical Settlement Amplitudes for Multiple Indicators (vi) Comparison with schemes that do not employ active learning or physical constraints The proposed solution is compared with solutions using ordinary deep neural networks, those employing only physical constraints without active learning, and those employing only active learning without physical constraints. Example results show that the proposed solution is superior in terms of MAPE near the threshold, the number of monotonicity violations of settlement risk, and the mean absolute error of the settlement limit.

[0068] Table 6 Comparison of different agent modeling schemes Note: DNN is the abbreviation for Deep Neural Network; MAPE is the Mean Absolute Percentage Error. The meanings of overall MAPE and MAPE near the threshold are consistent with those in Table 2.

[0069] (vii) Analysis of the technical effects of the embodiments In this embodiment, active learning and supplementation increased the proportion of samples near the threshold boundary from 18% to 68%, and reduced the MAPE near the threshold from 8.6% to 1.8%, indicating that the finite element samples were concentrated in the critical region that most affects the judgment of the settlement limit.

[0070] After introducing settlement risk monotonicity constraints, physical boundary constraints, and threshold boundary constraints into the physical constraint proxy model, the number of settlement risk monotonicity violations in the example scheme is reduced to 0, reducing predictions that do not conform to engineering principles.

[0071] Using multiple indicators to inversely determine the risk avoids the bias associated with a single indicator. Taking Table 5 as an example, if only the wheel-rail vertical force is considered, a limit of 10.1 mm may be obtained; however, after considering the vehicle body vertical acceleration, the limit is 9.2 mm, which better reflects the comprehensive risk of the vehicle-track-subgrade system.

Claims

1. A method for determining the limit of uneven settlement of high-speed railway subgrade based on a physical constraint active learning surrogate model, characterized in that, Includes the following steps: S1: Obtain high-speed railway engineering design information, train operation parameters, track structure parameters, roadbed structure parameters and foundation parameters, and establish a vehicle-track-settlement roadbed coupled finite element model based on the train operation parameters, track structure parameters, roadbed structure parameters and foundation parameters; S2: Construct a multi-condition parameter space, which includes settlement morphology parameters, structural parameters and velocity condition parameters, and encode the settlement morphology parameters, structural parameters and velocity condition parameters into settlement morphology codes, structural parameter codes and velocity condition codes, respectively. S3: Generate an initial working condition sample set based on the multi-working condition parameter space, call the vehicle-track-settlement subgrade coupled finite element model to perform dynamic calculations on the initial working condition sample set, extract multiple dynamic evaluation indicators, and form a high-fidelity sample library. S4: Train a physical constraint proxy model based on the high-fidelity sample library. The physical constraint proxy model takes the settlement morphology code, structural parameter code, and velocity condition code as input and the multi-dynamic evaluation index as output. The training loss function includes a data fitting term and a physical constraint term. S5: Construct a set of candidate working conditions, use the physical constraint surrogate model to predict the multi-dynamic evaluation index and prediction uncertainty corresponding to the candidate working conditions, and determine supplementary working conditions based on the prediction uncertainty, the degree to which the candidate working conditions are close to the threshold boundary of the evaluation index, and the contribution of the candidate working conditions to the parameter space coverage. S6: Call the vehicle-track-settlement subgrade coupled finite element model to perform dynamic calculations on the supplementary working condition, add the calculation results to the high-fidelity sample library, and update the physical constraint proxy model; S7: Repeat the candidate working condition prediction, supplementary working condition selection, finite element sampling calculation and physical constraint proxy model update until the preset convergence condition is met; S8: Using the updated physical constraint proxy model, under given train speed, structural parameters and settlement morphology, the minimum critical settlement amplitude that meets the threshold requirements of multiple dynamic evaluation indicators is inversely calculated, and the minimum critical settlement amplitude is determined as the subgrade uneven settlement limit.

2. The method according to claim 1, characterized in that, The coupled finite element model of vehicle-track-settlement subgrade includes a high-speed train system, a ballastless track system, and a settlement subgrade system. The high-speed train system includes a car body, bogies, and wheelsets. The primary suspension and secondary suspension are simulated between the car body and the bogies, and between the bogies and the wheelsets, respectively, through spring-damping units. The ballastless track system includes one or more of rails, fasteners, sleepers, track slabs, ballast slabs, or support layers. The settlement subgrade system includes one or more of the following: subgrade surface layer, subgrade bottom layer, subgrade body, and foundation.

3. The method according to claim 1, characterized in that, The settlement morphology parameters include one or more of the following: settlement type, settlement amplitude, settlement wavelength, settlement center location, settlement start and end locations, settlement influence range, maximum settlement slope, and maximum settlement curvature; the settlement type includes one or more of the following: misaligned settlement, cosine settlement, Gaussian trough settlement, bridge-road transition section settlement, tunnel-road transition section settlement, and local abrupt settlement.

4. The method according to claim 3, characterized in that, The settlement morphology coding includes one or more of the following: settlement type label coding, settlement amplitude normalization coding, settlement wavelength normalization coding, settlement location coding, settlement slope coding, settlement curvature coding, and settlement curve discrete point coding; wherein, the settlement curve along the line direction is discretized into several sampling points to form a settlement curve discrete vector, and the settlement curve discrete vector, together with settlement type, settlement amplitude, settlement wavelength, settlement slope, and settlement curvature, is used as the settlement morphology coding.

5. The method according to claim 1, characterized in that, The multi-dynamic evaluation indicators include vehicle safety indicators, ride comfort indicators, track structure dynamic response indicators, and roadbed dynamic response indicators; the vehicle safety indicators include one or more of wheel-rail vertical force, wheel-rail lateral force, derailment coefficient, and wheel load reduction rate; the ride comfort indicators include one or more of car body vertical acceleration and car body lateral acceleration; the track structure dynamic response indicators include one or more of rail vertical displacement, rail acceleration, track slab displacement, track slab acceleration, track slab stress, and support layer stress; the roadbed dynamic response indicators include one or more of roadbed vertical displacement, roadbed dynamic stress, and roadbed acceleration.

6. The method according to claim 1, characterized in that, The physical constraint surrogate model is one or more of the following: Gaussian process regression model, random forest model, gradient boosting tree model, support vector regression model, deep neural network model, graph neural network model, physical constraint neural network model, or ensemble learning model; the input of the physical constraint surrogate model is X = [ X s , X p , X v ],in X s Encoding the settlement pattern X p Encode the structural parameters. X v For speed condition encoding; the output of the physical constraint proxy model is Y = [ Y 1, Y 2, ..., Y m ], where Y is the predicted output vector of multiple dynamic evaluation indicators, Y 1, Y 2, ..., Y m , where are the predicted values ​​of each dynamic evaluation index, and m is the total number of output dynamic evaluation indices.

7. The method according to claim 1, characterized in that, The training loss function mentioned in step S4 is: L=L data +λ 1 L mono +λ 2 L bound +λ 3 L limit in, L For total training loss, L data The data fitting loss between the surrogate model's predicted values ​​and the high-fidelity sample calculation values. L mono To constrain the loss due to the monotonicity of settlement risk, L bound For physical boundary constraint loss, L limit To evaluate the threshold boundary constraint loss, λ 1. λ 2. λ 3 represents the weighting coefficient.

8. The method according to claim 1, characterized in that, The supplementary working conditions mentioned in step S5 are determined as follows: For each candidate working condition in the candidate working condition set, its prediction uncertainty index, threshold boundary proximity index, and parameter space coverage index are calculated, and the three are weighted and summed to obtain the comprehensive sampling index, as shown in the following formula: A ( x )= αU ( x )+ βB ( x )+ γC ( x ) in, x Indicates candidate operating conditions. U ( x ) is the candidate operating condition x The proxy model predicts uncertainty. B ( x ) is the candidate operating condition x The degree to which it approaches the threshold boundary of multiple dynamic evaluation indicators C ( x ) is the candidate operating condition x Contribution to parameter space coverage, α , β , γ These are the weighting coefficients for the prediction uncertainty index, the threshold boundary proximity index, and the parameter space coverage index, respectively. The comprehensive sampling indicators are sorted from largest to smallest, and the candidate working conditions with the highest ranking are selected as supplementary working conditions. The vehicle-track-settlement subgrade coupled finite element model is then used to perform supplementary sampling calculations.

9. The method according to claim 1, characterized in that, The step S8, which involves finding the minimum critical settlement amplitude that satisfies the threshold requirements of multiple dynamic evaluation indicators, specifically involves: for each dynamic evaluation indicator, solving for the critical settlement amplitude when the dynamic evaluation indicator reaches the corresponding threshold through binary search or monotonic interpolation within a preset settlement amplitude range, and determining the minimum value among the critical settlement amplitudes corresponding to each dynamic evaluation indicator as the roadbed uneven settlement limit. The evaluation indicator corresponding to this minimum value is identified as the control indicator.

10. A system for determining the limit of uneven settlement of high-speed railway subgrade based on a physical constraint active learning surrogate model, characterized in that, include: The model building module is used to acquire high-speed railway engineering design information, train operation parameters, track structure parameters, roadbed structure parameters and foundation parameters, and to establish a vehicle-track-settlement roadbed coupled finite element model; The sample generation module is used to construct a multi-condition parameter space including settlement morphology parameters, structural parameters and velocity condition parameters, generate an initial condition sample set, call the vehicle-track-settlement subgrade coupled finite element model for dynamic calculation, and form a high-fidelity sample library. The surrogate model training module is used to train a physical constraint surrogate model that includes data fitting terms and physical constraint terms by taking the settlement morphology code, structural parameter code, and velocity condition code as input and multiple dynamic evaluation indicators as output. The active learning supplementary sampling module is used to determine supplementary working conditions based on the surrogate model's prediction uncertainty, threshold boundary proximity, and parameter space coverage. It calls the vehicle-track-settlement subgrade coupled finite element model to perform supplementary sampling calculations and update the surrogate model. The limit inverse calculation module is used to inversely calculate the minimum critical settlement amplitude that meets the threshold requirements of multiple dynamic evaluation indicators under given train running speed, structural parameters and settlement morphology conditions. The results output module is used to output the settlement limit curve, settlement limit surface, and risk level.

11. The system according to claim 10, characterized in that, The active learning complementation module includes: Uncertainty evaluation unit, used to calculate the uncertainty of surrogate model prediction for candidate working conditions; The threshold boundary proximity evaluation unit is used to calculate the degree to which candidate working conditions approach the threshold boundaries of each evaluation index. The parameter space coverage evaluation unit is used to calculate the supplementary contribution of candidate working conditions to the parameter space coverage of existing high-fidelity samples. The comprehensive sampling index calculation unit is used to weight and synthesize the prediction uncertainty, threshold boundary proximity and parameter space coverage to obtain the comprehensive sampling index of each candidate working condition. The working condition sorting and selection unit is used to sort candidate working conditions from largest to smallest according to the comprehensive sampling index and select supplementary working conditions. The finite element sampling and scheduling unit is used to automatically modify the input parameters of the vehicle-track-settlement subgrade coupled finite element model, submit finite element calculation tasks, and extract calculation results.

Images