A method and system for calculating the preset values ​​of ballastless track that integrates temperature and load

Abstract

This application provides a method and system for calculating the pre-set values ​​of ballastless track by integrating temperature and load, relating to the field of ballastless track technology. The method includes: collecting real-time temperature field data and historical train load spectrum data of the target bridge section; constructing a coupled mechanical model of ballastless track and bridge structure for numerical simulation; fusing the simulated deformation estimate of the track structure with measured relative deformation data; performing state estimation based on the fused dataset; generating deformation state values ​​to constrain the ballastless track; and performing inversion calculations according to the track constraint conditions to obtain the pre-set values ​​of the ballastless track. This application solves the technical problem in the prior art where the reliance on static design parameters and idealized simulation models leads to pre-set values ​​that cannot reflect real environmental loads, further affecting the calculation accuracy of pre-set values ​​for ballastless track construction. It achieves matching between pre-set values ​​and the actual structural response, improving the accuracy of ballastless track pre-set value calculation.

Description

Technical Field

[0001] This application relates to the field of ballastless track technology, specifically to a method and system for calculating preset values ​​of ballastless track that integrates temperature and load. Background Technology

[0002] In the construction and design of ballastless track for high-speed railways, determining the pre-set values ​​is a crucial step in ensuring the smoothness of track geometry and structural durability during operation. Existing methods typically rely on static design parameters provided by specifications and idealized finite element simulation models to obtain one-time pre-set values ​​through open-loop calculations. However, the actual temperature field experienced by bridge sections exhibits significant spatiotemporal transient characteristics, and the ballastless track-bridge structure undergoes nonlinear time-varying behaviors during service, such as concrete creep, interlayer voids, and stiffness degradation. This means that the static design parameters and idealized finite element simulation models cannot accurately reflect the actual structural response. Deviations in the pre-set value calculation results may introduce defects in the early stages of track laying or accelerate deterioration due to cumulative deformation during long-term operation, thus posing a potential risk to the track's high smoothness and durability.

[0003] In summary, existing technologies suffer from the technical problem that, due to reliance on static design parameters and idealized simulation models, preset values ​​cannot reflect real environmental loads and actual structural conditions, further affecting the calculation accuracy and long-term service performance of ballastless track construction preset values. Summary of the Invention

[0004] The purpose of this application is to provide a method and system for calculating the pre-set values ​​of ballastless track that integrates temperature and load, in order to solve the technical problem in the prior art that the pre-set values ​​cannot reflect the real environmental load and actual structural state due to reliance on static design parameters and idealized simulation models, which further affects the calculation accuracy and long-term service performance of the pre-set values ​​for ballastless track construction.

[0005] To achieve the above objectives, this application provides a method and system for calculating the preset values ​​of ballastless track that integrates temperature and load.

[0006] Firstly, this application provides a method for calculating the pre-set values ​​of ballastless track by integrating temperature and load. This method is implemented through a system for calculating the pre-set values ​​of ballastless track by integrating temperature and load. The method includes: collecting real-time temperature field data and historical train load spectrum data of the target bridge section; constructing a coupled mechanical model of the ballastless track and bridge structure for numerical simulation to obtain a simulation estimate of track structure deformation; collecting measured relative deformation data of the track slab and the bridge; fusing the simulation estimate of track structure deformation with the measured relative deformation data to generate a fused dataset; performing state estimation based on the fused dataset; generating deformation state values ​​to constrain the ballastless track; and performing inversion calculations according to the track constraint conditions to obtain the pre-set values ​​of the ballastless track.

[0007] Optionally, spatial grid analysis is performed on the target bridge section to construct a temperature sensing network for continuous data acquisition and obtain continuous temperature distribution data; three-dimensional spatial analysis is performed based on the continuous temperature distribution data to construct real-time temperature field data; a dynamic update mechanism for train load spectrum is constructed to acquire train operation data in real time for incremental learning and construct historical train load spectrum data; multi-scale coupling is performed based on the real-time temperature field data and the historical train load spectrum data to construct the ballastless track-bridge structure coupled mechanical model.

[0008] Optionally, the continuous temperature distribution data is mapped to a spatial grid to construct a discrete node temperature dataset; multiple spatial coordinates are extracted based on the spatial grid as interpolation base points, and temperature values ​​are extracted based on the multiple spatial coordinates, using the temperature values ​​as interpolation base values; spatial analysis is performed on the interpolation base points to construct a spatial distance matrix, and radial analysis is performed on the interpolation base points to construct a radial base value matrix; the discrete node temperature dataset is linearly combined based on the interpolation base values ​​and the radial base value matrix to construct a three-dimensional continuous temperature field; heat conduction time delay compensation is performed based on the three-dimensional continuous temperature field to generate the real-time temperature field data.

[0009] Optionally, a multi-scale model hierarchical architecture is established for analysis to determine the macroscopic, mesoscopic, and mesoscopic scales. Based on the macroscopic scale, the ballastless track-bridge structure is divided to determine the bridge structure layer; based on the mesoscopic scale, the ballastless track-bridge structure is divided to determine the track structure layer; and based on the mesoscopic scale, the ballastless track-bridge structure is divided to determine the interface transition layer. Coupling constraints are applied based on the multi-scale model hierarchical architecture, and coupling constraint conditions are set, including interface continuity conditions and force balance conditions. The bridge structure layer, track structure layer, and interface transition layer are coupled with their degrees of freedom according to the interface continuity conditions and force balance conditions to construct a multi-scale coupled mechanical model. The real-time temperature field data is used as the thermodynamic driving input, and the historical train load spectrum data is used as the dynamic driving input to drive the multi-scale coupled mechanical model for verification, thus constructing the ballastless track-bridge structure coupled mechanical model.

[0010] Optionally, a multi-source sensing network for the relative deformation of the track slab and bridge is constructed. Measured relative deformation data is generated using the measured relative deformation data from the multi-source sensing network. The simulated deformation estimate of the track structure is spatiotemporally synchronized with the measured relative deformation data to obtain spatiotemporally aligned data. The simulated deformation estimate of the track structure and the measured relative deformation data are dynamically weighted and fused according to the spatiotemporally aligned data to generate a weighted dataset. Data confidence analysis is performed on the weighted dataset to obtain multiple real-time confidence features. The fusion weights of the weighted dataset are dynamically adjusted based on the multiple real-time confidence features to generate the fused dataset.

[0011] Optionally, the sampling time data of the measured relative deformation data is extracted, and the output time data of the track structure deformation simulation prediction is extracted; the sampling time data and the output time data are matched based on the time dimension to construct a target time reference; the measured relative deformation data is processed continuously according to the target time reference to generate a first data processing result; the track structure deformation simulation prediction is interpolated according to the target time reference to generate a second data processing result; the first data processing result and the second data processing result are synchronized in time to construct a time synchronization sequence; the finite element mesh node coordinates of the track structure deformation simulation prediction are extracted, and the sensor data coordinates of the measured relative deformation data are extracted; the finite element mesh node coordinates are mapped to the sensor data coordinates based on the spatial dimension to construct a spatial synchronization mapping relationship; the time synchronization sequence and the spatial synchronization mapping relationship are combined to generate the spatiotemporal aligned data.

[0012] Optionally, nonlinear state estimation is performed based on the fused dataset to generate deformable state values; nonlinear constraint optimization is performed according to the deformable state values ​​to construct track constraint conditions to constrain the ballastless track and determine adjustable spatial constraint information; multi-objective optimization is performed based on the adjustable spatial constraint information to generate multiple optimization parameters; inversion is performed based on the multiple optimization parameters to determine multiple preset value combinations for filtering and generating preset values ​​for the ballastless track.

[0013] Optionally, based on the fused dataset, a nonlinear analysis of structural deformation of the ballastless track is performed to construct a nonlinear state transition analysis channel and a nonlinear observation analysis channel; an unscented transformation is performed on the fused dataset to determine multiple target sampling points, and these multiple target sampling points are synchronized to the nonlinear state transition analysis channel for propagation to generate a first state transition prediction value; the multiple target sampling points are synchronized to the nonlinear observation analysis channel for propagation to generate a second observation prediction value; uncertainty analysis is performed based on the first state transition prediction value and the second observation prediction value to construct an uncertainty covariance matrix; the first state transition prediction value and the second observation prediction value are corrected according to the fused dataset and the uncertainty covariance matrix to generate the deformation state value.

[0014] Optionally, track smoothness constraint analysis is performed based on the deformation state values ​​to construct track smoothness constraint conditions; track structural force analysis is performed based on the deformation state values ​​to construct structural mechanics feasible domain constraint conditions; construction feasibility analysis is performed based on the deformation state values ​​to construct construction feasibility constraint conditions; the track smoothness constraint conditions, the structural mechanics feasible domain constraint conditions, and the construction feasibility constraint conditions are coupled to generate the adjustable spatial constraint information.

[0015] Secondly, this application also provides a system for calculating the pre-set value of ballastless track by integrating temperature and load, used to execute the method for calculating the pre-set value of ballastless track by integrating temperature and load as described in the first aspect. The system includes: a numerical simulation module for collecting real-time temperature field data and historical train load spectrum data of the target bridge section, constructing a coupled mechanical model of the ballastless track and bridge structure for numerical simulation, and obtaining a simulation estimate of track structure deformation; a data fusion module for collecting measured relative deformation data of the track slab and the bridge, fusing the simulation estimate of track structure deformation with the measured relative deformation data to generate a fused dataset; and a constraint inversion module for performing state estimation based on the fused dataset, generating deformation state values ​​to constrain the ballastless track, and performing inversion calculations according to the track constraint conditions to obtain the pre-set value of the ballastless track.

[0016] One or more technical solutions provided in this application have at least the following technical effects or advantages: By collecting real-time temperature field data and historical train load spectrum data of the target bridge section, a coupled mechanical model of ballastless track and bridge structure is constructed for numerical simulation to obtain the predicted deformation value of the track structure; measured relative deformation data of the track slab and the bridge are collected, and the predicted deformation value of the track structure is fused with the measured relative deformation data to generate a fused dataset; state estimation is performed based on the fused dataset to generate deformation state values ​​to constrain the ballastless track, and inversion calculation is performed according to the track constraint conditions to obtain the preset value of the ballastless track. In other words, by using the measured relative deformation data as a feedback anchor point, nonlinear state estimation is used to correct model deviations, and adaptive preset values ​​are output under multiple constraints. Since the uncertainty at the source cannot be completely eliminated, a robust fault tolerance and correction mechanism is established to ensure that the accuracy of the final preset value is not fatally affected, achieving precise matching between the preset value and the actual structural response, thereby improving the accuracy of the ballastless track preset value calculation and the overall performance of the ballastless track.

[0017] The above description is merely an overview of the technical solution of this application. To better understand the technical means of this application and to facilitate its implementation according to the description, and to make the above and other objects, features, and advantages of this application more apparent, specific embodiments of this application are described below. It should be understood that the content described in this section is not intended to identify key or important features of the embodiments of this application, nor is it intended to limit the scope of this application. Other features of this application will become readily apparent through the following description. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely exemplary. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0019] Figure 1 This is a flowchart illustrating the calculation method for the preset values ​​of ballastless track that integrates temperature and load in this application.

[0020] Figure 2 This is a schematic diagram of the ballastless track preset value calculation system that integrates temperature and load in this application.

[0021] Figure labeling: Numerical simulation module 11, data fusion module 12, constraint inversion module 13. Detailed Implementation

[0022] This application provides a method and system for calculating pre-set values ​​for ballastless track that integrates temperature and load. This addresses the technical problem in existing technologies where reliance on static design parameters and idealized simulation models leads to pre-set values ​​that fail to reflect real environmental loads and the actual structural state, further impacting the accuracy of pre-set values ​​calculations and long-term service performance of ballastless track. By using measured relative deformation data as feedback anchors, nonlinear state estimation is employed to correct model biases, and adaptive pre-set values ​​are output under multiple constraints. Since the uncertainty at the source cannot be completely eliminated, a robust fault-tolerance and correction mechanism is established to ensure that the accuracy of the final pre-set values ​​is not fatally affected. This achieves precise matching between the pre-set values ​​and the actual structural response, thereby improving the accuracy of ballastless track pre-set value calculations and the overall performance of the ballastless track.

[0023] The technical solutions of this application will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. It should be understood that this application is not limited to the exemplary embodiments described herein. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application. It should also be noted that, for ease of description, only the parts related to this application are shown in the accompanying drawings, not all of them.

[0024] Example 1, please refer to the appendix. Figure 1 This application provides a method for calculating the preset values ​​of ballastless track that integrates temperature and load. This method is applied to a system for calculating the preset values ​​of ballastless track that integrates temperature and load. The specific steps of this method are as follows: Real-time temperature field data and historical train load spectrum data of the target bridge section were collected to construct a coupled mechanical model of ballastless track-bridge structure for numerical simulation and obtain the simulation estimate of track structure deformation.

[0025] Furthermore, this application also includes the following steps: traversing the target bridge section to perform spatial grid analysis, constructing a temperature sensing network for continuous data acquisition, and obtaining continuous temperature distribution data; performing three-dimensional spatial analysis based on the continuous temperature distribution data to construct real-time temperature field data; constructing a dynamic update mechanism for the train load spectrum to acquire train operation data in real time for incremental learning, and constructing historical train load spectrum data; and performing multi-scale coupling based on the real-time temperature field data and the historical train load spectrum data to construct the ballastless track-bridge structure coupled mechanical model.

[0026] Furthermore, this application also includes the following steps: mapping the continuous temperature distribution data to a spatial grid to construct a discrete node temperature dataset; extracting multiple spatial coordinates as interpolation base points based on the spatial grid, extracting temperature values ​​based on the multiple spatial coordinates, and using the temperature values ​​as interpolation base values; calculating the interpolation base points for spatial analysis to construct a spatial distance matrix, performing radial analysis on the interpolation base points to construct a radial base value matrix; linearly combining the discrete node temperature dataset based on the interpolation base values ​​and the radial base value matrix to construct a three-dimensional continuous temperature field; and performing heat conduction time delay compensation based on the three-dimensional continuous temperature field to generate the real-time temperature field data.

[0027] Furthermore, this application also includes the following steps: establishing a multi-scale model hierarchical architecture for analysis to determine the macroscopic, mesoscopic, and mesoscopic scales; dividing the ballastless track-bridge structure based on the macroscopic scale to determine the bridge structure layer; dividing the ballastless track-bridge structure based on the mesoscopic scale to determine the track structure layer; dividing the ballastless track-bridge structure based on the mesoscopic scale to determine the interface transition layer; applying coupling constraints based on the multi-scale model hierarchical architecture and setting coupling constraint conditions, including interface continuity conditions and force balance conditions; coupling the bridge structure layer, track structure layer, and interface transition layer with degrees of freedom according to the interface continuity conditions and force balance conditions to construct a multi-scale coupled mechanical model; using the real-time temperature field data as a thermodynamic driving input and the historical train load spectrum data as a dynamic driving input to drive the multi-scale coupled mechanical model for verification, thus constructing the ballastless track-bridge structure coupled mechanical model.

[0028] Specifically, for the target bridge section, including all structural layers such as the air layer at a certain height above the bridge deck, the bridge top slab, bottom slab, web slab, track slab, and mortar layer, a three-dimensional solid model was created using finite element preprocessing software and divided into a uniform spatial mesh. The spatial coordinates of each mesh node were precisely recorded. Spatial mesh analysis refers to discretizing the bridge structure in three-dimensional space, dividing it into many small units, each with clearly defined spatial coordinates. Temperature sensors were embedded at key sections and depths of the bridge and track structures. The number of sensors was sufficient to cover the main dimensions of temperature field variation. All sensors continuously collected temperature data at a frequency of once per minute through a data acquisition instrument, forming continuous temperature distribution data.

[0029] Extract the precise spatial coordinates of all sensor locations, find the corresponding nodes in the spatial grid, and assign the current temperature value of the sensor to these nodes to form a discrete node temperature dataset. For grid nodes without sensors, their temperature values ​​are temporarily unknown and will be filled in later through interpolation. Use all grid nodes with measured temperature values ​​as interpolation base points, recording their spatial coordinates and temperature values; the temperature values ​​serve as the interpolation base values. In the spatial grid, those grid nodes with actual sensor installations and measured temperature values ​​are used as the base points for subsequent interpolation calculations. The measured temperature values ​​at the interpolation base points are used as the interpolation base values.

[0030] Calculate the Euclidean distance between any two interpolation base points to form a spatial distance matrix. This spatial distance matrix is ​​a matrix composed of the linear spatial distances between any two interpolation base points and is used to measure the spatial correlation between the base points. Perform radial analysis on the interpolation base points, selecting a radial basis function, such as the Gaussian function φ(r) = exp(-(ε...). r) 2 ), where r is the distance and ε is the shape parameter, typically a constant between 1 and 5, determined by the average grid spacing. Substituting each distance value in the spatial distance matrix into a Gaussian function yields a new matrix, the radial basis matrix. Each element in this matrix represents a weighting coefficient for the temperature influence between two corresponding basis points.

[0031] Based on the interpolation basis values ​​and the radial basis value matrix, a linear combination of discrete node temperature datasets is performed to solve a system of linear equations. The coefficient matrix is ​​the radial basis value matrix, with the right-hand side representing the temperature value of each basis point. The weight coefficients corresponding to each basis point are then obtained. For any target grid node whose temperature needs to be predicted, the distance from that node to all interpolation basis points is calculated. These distances are then converted into a radial basis value vector using the same radial basis function. Finally, the dot product of this vector and the obtained weight coefficients yields the predicted temperature value for that node. By traversing all grid nodes without measured data, the temperature value of each node on the entire spatial grid is obtained, thus constructing a three-dimensional continuous temperature field.

[0032] Because heat conduction in concrete is limited, temperature changes inside the structure lag behind those at the surface. To obtain the actual internal temperature at the current moment, compensation based on the heat conduction equation is required. Specifically, a one-dimensional or three-dimensional differential heat conduction model of the structure is first established, and a historical measured surface temperature sequence over a period of time (e.g., the past 6 hours) is input. The temperature at each depth inside the structure at the current moment is then deduced by solving the heat conduction equation. Due to the thermal inertia of materials such as concrete, changes in its internal temperature lag behind changes in surface or ambient temperature. Time-delay compensation corrects the calculated or measured temperature field in the time dimension to more accurately reflect the true temperature distribution inside the structure. The compensated temperature values ​​replace the internal node temperatures in the original interpolation results, ultimately generating real-time temperature field data with high spatiotemporal accuracy.

[0033] For example, 45 grid nodes containing sensors are used as interpolation base points, each with three-dimensional coordinates and a measured temperature value. For instance, the coordinates of a node on the center surface of the plate are (2.8, 1.25, 0.2), and the coordinates of a node on the sunny side of the plate corner are (0, 0, 0.2). The distance between them is calculated to be 3.066 meters using Euclidean distance. The Gaussian function φ(r) = exp(-(ε) is chosen. r) 2 Taking ε=2, we calculate φ(r)=1.3e -16 The value is almost zero, indicating that the influence of long distances is negligible. After solving the linear equations to obtain the weight coefficients of each base point, the temperature of any node within the slab is predicted. For example, the node with coordinates (2.8, 1.25, 0.08) is calculated to have a temperature of 46.8℃. The surface temperature is known to be 52.3℃ at 14:00, 51.0℃ at 13:30, and 49.5℃ at 13:00. Based on the heat conduction equation and the thermal diffusivity of concrete (approximately 0.5 × 10⁻⁶), the temperature is determined. -6 m 2 The time lag at a depth of 0.08 meters is calculated to be approximately 45 minutes. Therefore, the actual temperature at a depth of 0.08 meters at 14:00 should be approximately equal to the surface temperature at 13:15, which is 50.2℃. After correction, the temperature at this point is revised from the interpolated 46.8℃ to 50.2℃.

[0034] Axial force sensors and strain gauges are installed on the track structure of the target bridge section to monitor and record information such as train number, axle load, wheelbase, speed, and passage time for each passing train in real time. An incremental learning algorithm is used, with newly added data each day only used to update the statistical parameters of the load spectrum: for example, calculating the maximum axle load for the day and the passing frequency of each axle load interval, and then accumulating these statistics into the historical total. A sliding time window is set, and old data outside the window is weighted and attenuated or removed to reflect recent trends in operational load changes. Whenever a new batch of train passing data is collected, statistical analysis is performed on the new data to calculate the frequency of occurrence, axle load distribution, speed distribution, and other characteristics of various train types within the current period. These short-term statistical characteristics are then merged and updated with the long-term statistical characteristics of the historical load spectrum using a Bayesian update method, assigning certain weights to the new data. This allows the load spectrum to smoothly reflect the latest trends in operational load changes without recalculating all historical data. Historical train load spectrum data is a statistical set of data that records the load characteristics of all trains passing through the target bridge section over a period of time. It includes not only the axle load, wheelbase, and speed of individual trains, but more importantly, the frequency and probability distribution of different train combinations, different train formations, and different speed levels.

[0035] Based on the geometric dimensions and mechanical properties of the ballastless track-bridge structure, a multi-scale hierarchical model architecture is established. This involves modeling the complex ballastless track-bridge structure in layers according to different scales of geometric features and mechanical behavior, and establishing a numerical analysis framework with coupling relationships between these layers. These layers include macroscopic, mesoscopic, and mesoscopic scales. The macroscopic scale represents the overall structural scale, used to simulate the overall deformation and internal forces of the entire bridge. The mesoscopic scale represents the scale of the internal component layers of the structure, used to simulate the local behavior of each structural layer of the ballastless track. The mesoscopic scale is a scale between the mesoscopic and microscopic scales, used to simulate the interface transition layer between two different structural layers.

[0036] Based on the macroscopic scale, the entire bridge is divided into bridge structural layers, providing overall support stiffness and boundary conditions. Based on the microscopic scale, the rails, fasteners, track slabs, self-compacting concrete layers, and base plates are divided into track structural layers, responsible for bearing train loads and transferring them to the bridge. Based on the mesoscopic scale, the contact surfaces between the track slabs and self-compacting concrete, between the self-compacting concrete and base plates, and between the base plates and the top surface of the beam are divided into interface transition layers, with each interface transition layer employing an independent contact constitutive model.

[0037] The macroscopic, mesoscopic, and latitudinal models are precisely aligned in space. Coupling constraints are defined at the model boundaries, including interface continuity and force equilibrium conditions. A series of paired nodes are selected in the overlapping region. For each pair of nodes, the interface continuity condition is applied, forcing these paired nodes to have equal displacements in all three translational degrees of freedom. Specifically, when the bridge node in the macroscopic model and the bottom node of the base plate in the mesoscopic model coincide in spatial coordinates, their vertical and horizontal displacements must be equal. Simultaneously, the forces transmitted between these paired nodes must satisfy the force equilibrium condition, meaning the force on one node is equal in magnitude and opposite in direction to the force on another node.

[0038] In finite element method (FEM) software, multi-point constraints are used to couple the nodal degrees of freedom at the interfaces of the bridge structure layer, track structure layer, and interface transition layer. Nodes of the macroscopic model at the interface are selected as master nodes, and corresponding nodes of the mesoscopic or microscopic model are selected as slave nodes. Constraint equations are established such that the displacement of the slave node equals the displacement of the master node, i.e., displacement degree of freedom is coupled. For force equilibrium, the reaction force is automatically calculated by the FEM software. Nodes with the same spatial position at the interface in models of different scales are linked by constraint equations to ensure that these nodes maintain consistent displacement or satisfy force transmission relationships during calculation, thus completing the construction of a multi-scale coupled mechanical model. Specifically, after mesh generation, the coordinates of all nodes on the top surface of the bridge structure layer and the bottom surface of the base plate are extracted. Since the mesh size may differ, a spatial search algorithm is used to find each pair of closest nodes and establish master-slave node pairs. Typically, nodes of the macroscopic model are set as master nodes, and nodes of the mesoscopic model are set as slave nodes. For each master-slave node pair, constraint equations are established; under ideal continuity conditions, the displacement of the slave node equals the displacement of the master node. If the mesh does not match, the displacement of the slave node is equal to the displacement obtained by interpolation of the shape function of the element containing the master node. During the solution process, the finite element software automatically achieves force balance based on the sum of the reactions on the slave nodes being equal to the forces acting on the master nodes, without requiring the user to explicitly set the equations. For the mesoscopic interface layer between the track slab and the self-compacting concrete, a contact pair algorithm is used. The bottom surface of the track slab is set as the master surface, and the top surface of the self-compacting concrete is set as the slave surface. The contact properties are defined as follows: normal behavior allows for re-contact after separation, and tangential behavior uses penalized friction. In this case, the degree of freedom coupling is not a simple equality of displacements, but rather the transmission of forces is achieved through contact constraints. Penalized friction is a numerical method for realizing Coulomb friction in the finite element method. It introduces a penalty stiffness to allow the contact surfaces to produce small elastic slips before sliding occurs, rather than strictly requiring the static friction force to reach a threshold before sliding.

[0039] Real-time temperature field data is used as the thermal driving input, and historical train load spectrum data is used as the dynamic driving input. These are dynamically applied to the rail in a multi-scale coupled mechanical model in the form of moving concentrated forces or pressure distributions. In other words, real-time temperature field data is imported into the finite element software as a predefined field, automatically calculating the temperature at each element integration point, and then calculating the thermal strain based on the coefficient of thermal expansion: Thermal strain = Coefficient of thermal expansion × (Current temperature - Reference temperature). The reference temperature is usually the construction lock-in temperature, such as 20℃. Temperature increases cause expansion, which, if constrained, generates compressive stress; temperature decreases cause contraction, generating tensile stress. Historical train load spectrum data is converted into moving concentrated forces or moving uniformly distributed forces. A representative load case is selected from the load spectrum, simplifying each wheelset into a single concentrated force acting perpendicularly on the top surface of the rail. In the transient dynamic analysis, a time step of 0.001 seconds is set, and the moving loads are input in tabular form: at each time step, different wheelsets are located at different positions, and forces of corresponding magnitudes are applied. The moving load is transferred to the track slab through the fasteners, and then to the base plate and bridge through the interface layer, causing dynamic deformation and vibration of the entire system.

[0040] Run this thermo-mechanical coupled transient analysis to calculate the stress, deformation, and internal force response of the multi-scale coupled mechanical model under the combined effects of temperature and train load. Compare the simulation results with the measured values ​​from the field. If the deviation is within the allowable range, the multi-scale coupled mechanical model is considered to be correctly constructed; otherwise, adjust the interface parameters (such as friction coefficient and bonding stiffness) or material damping coefficient until the simulation results match the measured data. Specifically, output the vertical displacement time history curves of key measuring points from the multi-scale coupled mechanical model; install displacement gauges, strain gauges, and accelerometers at the same locations on site, and simultaneously record the measured values ​​under the same temperature conditions and when the train passes. Calculate the relative error between the simulated and measured values. If the error exceeds 10%, adjust the uncertain parameters in the model, such as the interface friction coefficient, fastener stiffness, and material damping. Repeat the simulation until the error is within an acceptable range, such as within 2%.

[0041] The validated model is the coupled mechanical model of ballastless track-bridge structure, used to calculate the deformation of the track structure under the combined action of temperature load and train load. Real-time temperature field at the moment of maximum temperature gradient throughout the day, along with the most unfavorable train load, is used. Transient dynamic analysis is performed through the coupled mechanical model of ballastless track-bridge structure, with the calculation time covering the entire train passage process. Vertical displacement of the rail top surface, vertical displacement of the track slab corners, vertical displacement of the track slab mid-section, and inter-layer relative slip are extracted from the simulation results to obtain the predicted deformation value of the track structure. The predicted deformation value of the track structure is the vertical and lateral displacement of key points of the track structure calculated by the coupled mechanical model of ballastless track-bridge structure under the combined action of temperature and load.

[0042] A dynamic update mechanism for the train load spectrum was constructed, enabling load input to no longer rely on static design spectra but instead continuously learn from real operational data. This allows for the capture of actual characteristics such as overweight trains, speed changes, and frequency evolution, significantly improving the realism and timeliness of load conditions. A multi-scale hierarchical architecture (macro-meso-macro) is adopted, ensuring accurate simulation of overall bridge deformation while finely characterizing the stress-strain distribution of each structural layer of the track. It also simulates nonlinear behaviors such as interface layer delamination and slippage. Compared to a single-scale model, with the same computational resources, the computational accuracy is improved by approximately 30% to 50%, while the computational load increases by only about 20%.

[0043] Collect measured relative deformation data between the track slab and the bridge, and fuse the predicted deformation value of the track structure with the measured relative deformation data to generate a fused dataset.

[0044] Furthermore, this application also includes the following steps: constructing a multi-source sensing network for the relative deformation of the track slab and the bridge; constructing measured relative deformation data using the measured relative deformation data from the multi-source sensing network; synchronizing the simulated deformation estimate of the track structure with the measured relative deformation data in time and space to obtain spatiotemporally aligned data; dynamically weighting and fusing the simulated deformation estimate of the track structure with the measured relative deformation data according to the spatiotemporally aligned data to generate a weighted dataset; performing data confidence analysis based on the weighted dataset to obtain multiple real-time confidence features; and dynamically adjusting the fusion weights of the weighted dataset based on the multiple real-time confidence features to generate the fused dataset.

[0045] Furthermore, this application also includes the following steps: extracting the sampling time data of the measured relative deformation data and extracting the output time data of the track structure deformation simulation prediction; matching the sampling time data and the output time data based on the time dimension to construct a target time reference; performing continuous processing on the measured relative deformation data according to the target time reference to generate a first data processing result; performing data interpolation on the track structure deformation simulation prediction according to the target time reference to generate a second data processing result; synchronizing the first data processing result and the second data processing result in time to construct a time synchronization sequence; extracting the finite element mesh node coordinates of the track structure deformation simulation prediction and extracting the sensor data coordinates of the measured relative deformation data; mapping the finite element mesh node coordinates to the sensor data coordinates based on the spatial dimension to construct a spatial synchronization mapping relationship; combining the time synchronization sequence and the spatial synchronization mapping relationship to generate the spatiotemporal aligned data.

[0046] Specifically, a variety of sensors are installed between the track slabs and the bridge in the target bridge section, and a heterogeneous sensor network is deployed. For example, wire-type displacement gauges are installed under the four corners of each track slab, laser displacement gauges are installed in the middle of the slab, and differential transformer displacement gauges are installed between the side of the track slab and the bridge stop. All sensors are continuously collected by a synchronous data acquisition instrument at a fixed sampling frequency, and the timestamp of each sampling moment is recorded to obtain the measured relative deformation data.

[0047] Extract the sampling time data of the measured relative deformation data, that is, the specific time point when the sensor collects data, and extract the output time data of the track structure deformation simulation prediction, that is, the time point corresponding to the output result of the finite element simulation model. After matching the sampling time of the measured data and the output time of the simulation data, a unified time axis is determined, that is, the target time reference, and the time points on this time axis are the union of the two time points.

[0048] Since the measured data only has values ​​at the sampling time and not at other times on the target time base, the measured relative deformation data is processed to be continuous. A smooth cubic spline curve is constructed with the sampling time as the independent variable and the measured deformation value as the dependent variable. Substituting each time point on the target time base into this curve, the corresponding deformation value is calculated, yielding the first data processing result. Simulation data only has values ​​at the output time and also needs to be interpolated onto the target time base. Since simulation data is usually relatively smooth, linear interpolation is sufficient to meet the accuracy requirements. For a specific time point on the target time base, such as 0.001s, two adjacent simulation output times are found, such as 0.000s and 0.005s. The simulation deformation values ​​at these two times are taken and linearly weighted according to the time ratio to calculate the simulation deformation value at 0.001s. This process is repeated for all target time base points to obtain a sequence of simulation deformation values, called the second data processing result. The first data processing result and the second data processing result are merged at the same time point to form a time synchronization sequence. Each row of the time synchronization sequence contains time, measured relative deformation data, and simulation estimate of track structure deformation.

[0049] The coordinates of the finite element mesh nodes, i.e., the three-dimensional coordinates of all mesh nodes, are derived from the finite element model to obtain the sensor data coordinates of the measured relative deformation data. Simultaneously, the installation coordinates of each sensor are recorded, yielding the sensor data coordinates of the relative deformation data. Since the mesh nodes and sensor positions cannot perfectly coincide, a model node representing each sensor needs to be found. All model nodes are traversed, and the spatial distance from each node to a given sensor is calculated. The model node with the smallest distance is identified as the mapping node for that sensor, and the mapping pair of sensor ID and model node ID is recorded. This process is repeated for all sensors, establishing a spatial synchronization mapping relationship. Combining the temporal synchronization sequence with the spatial synchronization mapping relationship yields spatiotemporally aligned data. For each regular time point and each sensor, the corresponding model node can be found through the spatial mapping relationship, thus determining the measured deformation value and the simulated deformation prediction of the model node at a given moment and sensor location.

[0050] The simulated deformation estimate and the measured relative deformation data of the track structure are dynamically weighted and fused according to the spatiotemporal aligned data. For each spatiotemporal point, a weighted average method is used to calculate the fused deformation value. The initial weights are set to 0.5 for the measured value and 0.5 for the simulated value. These weights are dynamically adjusted based on the results of subsequent confidence analysis. First, a fusion is performed using the initial weights to obtain a preliminary weighted dataset. The fused deformation value equals the measured value multiplied by the measured weight plus the simulated value multiplied by the simulated weight. This calculation is performed for all spatiotemporal points to generate the initial weighted dataset. For example, at time 0.150 seconds, the measured value is 1.75 mm, the simulated value is 1.77 mm, and the fused value is 1.76 mm; at time 0.151 seconds, the measured value is 1.78 mm, the simulated value is 1.78 mm, and the fused value is 1.78 mm, resulting in the preliminary weighted dataset.

[0051] Data confidence analysis is performed on the weighted dataset to quantitatively assess the uncertainty, noise level, and anomaly degree of each data source, obtaining quantitative indicators reflecting its reliability. For measured data, the noise level is calculated, and the standard deviation is calculated using measured values ​​taken over a static period. For simulation data, the model uncertainty is calculated. Under validated operating conditions, the root mean square error between simulated and measured values ​​is 0.05 mm; near model boundaries, such as beam ends and plate corners, this error may increase to 0.12 mm. An error distribution map is pre-defined based on spatial location; the larger the error, the lower the confidence level. For measured data, if the sensor does not update for three consecutive time points, the confidence level gradually decreases. A confidence feature value is calculated for each data source at each spatiotemporal point, ranging from 0 to 1.

[0052] The fusion weights of the weighted dataset are dynamically adjusted based on multiple real-time confidence features. The measured weight equals the measured confidence level divided by the sum of the measured and simulated confidence levels; the simulated weight equals the simulated confidence level divided by the sum of the measured and simulated confidence levels. Data sources with higher confidence levels receive greater weights. For example, if the measured confidence level at a certain spatiotemporal point is 0.95 and the simulated confidence level is 0.80, the measured weight is calculated to be 0.543, and the simulated weight is 0.457. Then, the fusion deformation value is recalculated: Fusion value = Measured value × 0.543 + Simulated value × 0.457. For obviously anomalous measured values, such as sudden spikes, the measured confidence level is forcibly set to 0.01, making its weight extremely low. This ensures that the fusion value almost entirely depends on the simulated value, avoiding contamination of the results by anomalous data. This dynamic weighted fusion is performed on all spatiotemporal points to generate a complete fusion dataset containing the final fusion deformation value at each time point and spatial node. Through dynamic weighted fusion, the authenticity of the measured data and the completeness of the simulated data are effectively combined. Real-world data is accurate but sparse and may contain noise, while simulation data is continuous and complete but suffers from model bias. The fused dataset maintains full spatial node coverage and uses measured values ​​to correct simulation biases at nodes with sensors.

[0053] Based on the fused dataset, state estimation is performed to generate deformable state values ​​to constrain the ballastless track. Inversion calculations are then performed according to the track constraint conditions to obtain the preset values ​​for the ballastless track.

[0054] Furthermore, this application also includes the following steps: performing nonlinear state estimation based on the fused dataset to generate deformable state values; performing nonlinear constraint optimization according to the deformable state values ​​to construct track constraint conditions to constrain the ballastless track and determine adjustable spatial constraint information; performing multi-objective optimization based on the adjustable spatial constraint information to generate multiple optimization parameters; performing inversion solution based on the multiple optimization parameters to determine multiple preset value combinations for screening and generating preset values ​​for the ballastless track.

[0055] Furthermore, this application also includes the following steps: performing nonlinear analysis of structural deformation of the ballastless track based on the fused dataset, constructing a nonlinear state transition analysis channel and a nonlinear observation analysis channel; performing an unscented transformation on the fused dataset to determine multiple target sampling points, synchronizing the multiple target sampling points to the nonlinear state transition analysis channel for propagation, generating a first state transition prediction value; synchronizing the multiple target sampling points to the nonlinear observation analysis channel for propagation, generating a second observation prediction value; performing uncertainty analysis based on the first state transition prediction value and the second observation prediction value, constructing an uncertainty covariance matrix; correcting the first state transition prediction value and the second observation prediction value according to the fused dataset and the uncertainty covariance matrix, generating the deformation state value.

[0056] Furthermore, this application also includes the following steps: performing track smoothness constraint analysis based on the deformation state values ​​to construct track smoothness constraint conditions; performing track structural force analysis based on the deformation state values ​​to construct structural mechanics feasible domain constraint conditions; performing construction feasibility analysis based on the deformation state values ​​to construct construction feasibility constraint conditions; and coupling the track smoothness constraint conditions, the structural mechanics feasible domain constraint conditions, and the construction feasibility constraint conditions to generate the adjustable spatial constraint information.

[0057] Specifically, due to interlayer contact and material nonlinearity in ballastless track structures, the relationship between deformation and load is not a simple linear proportion, thus requiring nonlinear analysis. The state vector is determined, and the state variables should comprehensively describe the key deformation behaviors of the ballastless track structure, such as the vertical displacement of the four corners of the track slab, the vertical displacement within the slab, the clearance height between the track slab and the mortar layer, and the compression of the fastener system. The state transition channel describes the evolution of these states over time. Driven by temperature changes and train loads, the state transition is nonlinear. The observation channel describes the relationship between the state variables and the deformation values ​​in the fused dataset. Each observation in the fused dataset is typically a nonlinear combination of state variables. The nonlinear state transition analysis channel is a nonlinear function xk=f(x{k-1},uk,wk) describing the state evolution. Here, uk is the known input, such as real-time temperature field data and train load data at the current moment; wk is the process noise, representing model error and unmodeled dynamics; and k is the current moment. The function f can utilize a reduced-order surrogate model of the aforementioned multi-scale coupled mechanics model. Its construction needs to reflect the main dynamic characteristics of the ballastless track under temperature and load, such as nonlinear restoring force and damping characteristics. The nonlinear observation and analysis channel is a nonlinear function zk=h(xk,vk) that describes how the state is observed. Here, vk is the observation noise. The function h is usually a mapping matrix that extracts the displacement components corresponding to the sensor positions from the full state vector. If the observation includes nonlinear quantities, such as strain, then h needs to include the corresponding physical relationships.

[0058] An unscented transformation is performed on the fused dataset to generate a set of sampling points near the current state estimate. Assuming the current state vector has dimension n, the mean vector and covariance matrix of the current state estimate are calculated. 2n+1 sampling points are generated according to a symmetric sampling rule: the first point is the mean itself; the remaining 2n points are distributed around the mean, offset by a certain distance along each principal axis, the distance being related to the square root of the covariance matrix and the scaling parameter. Each of these sampling points has a corresponding weight. These sampling points capture the first and second moments of the state distribution, i.e., the mean and covariance, and when propagated through a nonlinear function, they can approximate the true posterior distribution with third-order accuracy.

[0059] Substituting each sampling point into the nonlinear state transition function of the nonlinear state transition analysis channel, the predicted state value for the next time step corresponding to each sampling point is calculated. For example, for a sampling point, the plate angle displacement at the next time step is predicted based on the current plate angle displacement and temperature change rate. After propagation for all sampling points, a set of predicted sampling points is obtained. Then, according to the weight of each sampling point, these predicted sampling points are weighted and averaged to obtain the predicted mean of the state at the next time step; simultaneously, the weighted covariance matrix of these predicted sampling points relative to this mean is calculated to obtain the state prediction covariance. This mean vector and covariance matrix are collectively called the first state transition prediction value, representing the estimation of the state at the next time step and its uncertainty based solely on the system model. The first state transition prediction value is calculated by weighting and averaging the obtained point set after propagating the target sampling points through the nonlinear state transition channel, and it reflects the state estimation result without actual data correction.

[0060] The original sampling points are substituted into the nonlinear observation function of the nonlinear observation analysis channel to calculate the predicted observation value for each sampling point, i.e., the predicted fused deformation data. For example, for a sampling point, the relative displacement at the sensor location is calculated based on the predicted plate corner displacement and bridge deformation. After propagation through all sampling points, a set of predicted observation sampling points is obtained. A weighted average is taken from these points to obtain the mean of the predicted observations; and the weighted covariance matrix of these points relative to this mean is calculated to obtain the predicted observation covariance. Simultaneously, the cross-covariance matrix between the state prediction and the predicted observations is calculated. These results are collectively referred to as the second predicted observation value. The second predicted observation value is calculated by weighting the point set obtained after propagating the target sampling points through the nonlinear observation channel, calculating the mean and covariance of the predicted deformation values, and comparing them with the observed values ​​in the actual fused dataset.

[0061] An augmented uncertainty covariance matrix is ​​constructed by combining the state prediction covariance, observation prediction covariance, and cross-covariance matrices. This matrix represents the uncertainty inherent in the state prediction, the uncertainty inherent in the observation prediction, and the correlation between the state and observations. The uncertainty covariance matrix is ​​a block matrix: the top-left block represents the state prediction covariance, the bottom-right block represents the observation prediction covariance, and the bottom-left and top-right blocks represent the cross-covariance and its transpose. The diagonal elements of the covariance matrix represent the variance (magnitude of uncertainty) of each variable, while the off-diagonal elements represent the correlation between variables.

[0062] Based on the fused dataset, the actual observation values ​​at the current moment are obtained, and the difference between the actual observation values ​​and the observed prediction mean is calculated. This reflects the deviation between the simulation estimate and the actual deformation of the track structure. The Kalman gain matrix is ​​calculated using the cross-covariance matrix and the inverse of the observed prediction covariance matrix. The Kalman gain determines the degree to which the predicted state should be corrected. The predicted state mean is corrected by adding the Kalman gain multiplied by the difference. Simultaneously, the predicted state covariance is corrected by subtracting the Kalman gain multiplied by the transpose of the cross-covariance matrix. The corrected state mean and covariance represent the deformation state value at the current moment. This value integrates the physical predictions of the system model and the observation information from the fused dataset, considering their respective uncertainties, and is therefore the optimal estimate.

[0063] Key geometric parameters are extracted from the deformation state values, such as the deviation of the current track slab angle from the design elevation, the height difference between joints of adjacent track slabs, and the undulations of the rail top surface along the track direction. The track smoothness acceptance standards for the corresponding speed level are consulted, and these standards are converted into mathematical inequalities regarding preset values. For example, if the measured deviation of the current track slab angle is -0.5mm (i.e., below the design elevation), the preset value must be set to +1.2mm or higher to ensure that the final height difference does not exceed the limit. In specific calculations, it is necessary to consider the deformation under temperature and load after setting the preset value, ensuring that the smoothness in the final operating state meets the specifications. Therefore, the constraint condition is usually expressed as the preset value plus the deformation state value (the expected increment under future loads) must be within the allowable range of smoothness. This results in a set of linear or nonlinear inequalities regarding the preset values, constituting the track smoothness constraint conditions. The track smoothness constraint conditions are a set of mathematical inequalities derived from smoothness constraint analysis. For example, the height difference between adjacent track slab ends must not exceed 1 mm; the unevenness of the rail height measured chordally every 10 meters must not exceed 2 mm; and the height difference in a horizontal triangular pit with a length of 3 meters must not exceed 1.5 mm. These constraints limit the range of preset values.

[0064] The goal of structural force analysis is to ensure that pre-set values ​​do not lead to excessive structural stress. A stress-strain relationship model for each structural layer of the ballastless track is established, using deformation state values ​​as initial conditions. Then, a pre-set value is assumed—the amount artificially raised or lowered during construction—and the extreme stress values ​​of key components such as the track slab, mortar layer, base plate, and fasteners are calculated under temperature loads and train loads. The feasible region constraints of the structural mechanics require that the maximum tensile stress corresponding to the pre-set value ≤ the design value of concrete tensile strength; the maximum compressive stress ≤ the design value of compressive strength; the fastener compression ≤ the maximum allowable compression of the fastener; and the mortar layer stress ≤ the mortar strength, etc., constituting the feasible region constraints of the structural mechanics. These constraints ensure that the deformation state corresponding to the pre-set value does not cause the structural stress to exceed the material's allowable value.

[0065] The feasibility analysis considers the actual on-site construction capabilities, including the adjustment range of the fine-tuning claw, the pouring gap of the self-compacting concrete, the adjustment allowance of the fasteners, and the construction temperature restrictions. It calculates the allowable range of the preset values ​​under construction conditions, forming the constraints for construction feasibility. For example, the spatial gap between the bottom surface of the track slab and the top surface of the base plate after the preset values ​​are set must be between 20mm and 50mm; the adjustment amount of the fine-tuning claw must not exceed the maximum stroke; and the height of the cavity at the bottom of the slab must not be less than the specified value when pouring self-compacting concrete.

[0066] The track smoothness constraints, structural mechanics feasible region constraints, and construction feasibility constraints are coupled simultaneously, and their intersection is taken to form a comprehensive feasible region. The coupling process is typically achieved by combining multiple inequalities into a single constraint set, where no constraint can be violated. Adjustable spatial constraint information is the final constraint set obtained after coupling, describing the reasonable range within which preset values ​​can be adjusted while satisfying all safety, smoothness, and construction requirements.

[0067] The objective functions of multi-objective optimization typically include minimizing track geometry deviations, minimizing fastener pad adjustment, maximizing structural fatigue life, and minimizing construction costs. These objectives are often conflicting; for example, pursuing better ride comfort may require larger preset values, but this increases construction difficulty. Optimization variables include preset values ​​for each plate corner and fastener pad thickness. A multi-objective evolutionary algorithm is used to search within the feasible region, generating a set of Pareto optimal solutions. Each solution corresponds to a set of optimization parameters, i.e., a combination of preset values, reflecting the trade-offs between different objectives. For example, solution A optimizes ride comfort but has higher construction costs, while solution B minimizes costs but has slightly lower ride comfort. Running parameters are configured for the selected multi-objective optimization algorithm, including population size, number of iterations, crossover and mutation probabilities, and penalty function coefficients.

[0068] The search space is defined by the feasible region of adjustable spatial constraints, and multiple objectives are optimized simultaneously. A series of preset value combinations are iteratively generated, each corresponding to a feasible adjustment scheme. After sufficient iterations, the search converges to a Pareto optimal frontier. Each solution on the frontier represents a specific trade-off among multiple objectives; for example, one solution has a small adjustment amount but also a small smoothness reserve, while another has a large adjustment amount but excellent smoothness. From the numerous solutions on the Pareto optimal frontier, a final preset value for the ballastless track is selected based on engineering experience and actual needs. If the decision-maker has a clear priority for a certain objective, such as minimizing the adjustment amount while meeting the minimum safety reserve for smoothness, this can be used for selection. A solution that performs relatively evenly across multiple objectives without significant weaknesses is selected. Engineers select from several candidate solutions, considering non-model-based factors such as the construction unit's equipment capabilities, schedule, and cost. The selected preset value combinations are organized into the format required for construction, typically a table or list, clearly listing the lateral, longitudinal, and vertical adjustment amounts for each track slab and each fastener position. The pre-set value for ballastless track is the final output target elevation value for the track slab used in the fine-tuning stage of construction. Based on this pre-set value, on-site workers use fine-tuning claws to lift the track slab to the designated elevation, and then pour self-compacting concrete to lock it in place. The pre-set value refers to the vertical displacement of the track slab during the fine-tuning stage, achieved by lifting or lowering it using fine-tuning claws; a positive value indicates lifting, and a negative value indicates lowering. This pre-set value ensures that the initial alignment of the track slab after being locked with self-compacting concrete can compensate for deformations caused by temperature, load, and long-term creep during operation, thereby guaranteeing that the geometry of the operating track meets the smoothness requirements.

[0069] Employing multi-objective optimization instead of single-objective optimization allows for the simultaneous consideration of the inherent trade-offs between different engineering objectives, generating a Pareto front for decision-makers to choose from, and avoiding the subjectivity of human weighting. Optimization based on adjustable spatial constraints ensures that all candidate preset value combinations are within a safe, feasible, and smooth range, preventing violations of specifications or construction infeasibility.

[0070] In summary, the method for calculating the pre-set values ​​of ballastless track by integrating temperature and load provided in this application has the following technical effects: By collecting real-time temperature field data and historical train load spectrum data of the target bridge section, a coupled mechanical model of the ballastless track and bridge structure is constructed for numerical simulation to obtain the simulation estimate of track structure deformation; measured relative deformation data of the track slab and the bridge are collected, and the simulation estimate of track structure deformation is fused with the measured relative deformation data to generate a fused dataset; based on the fused dataset, state estimation is performed to generate deformation state values ​​to constrain the ballastless track, and inversion calculation is performed according to the track constraint conditions to obtain the pre-set values ​​of the ballastless track. In other words, by using the measured relative deformation data as a feedback anchor point, nonlinear state estimation is used to correct model deviations, and adaptive pre-set values ​​are output under multiple constraints. Since the uncertainty at the source cannot be completely eliminated, a robust fault tolerance and correction mechanism is established to ensure that the accuracy of the final pre-set value is not fatally affected, achieving precise matching between the pre-set value and the actual structural response, thereby improving the accuracy of the ballastless track pre-set value calculation and the overall performance of the ballastless track.

[0071] Example 2: Based on the same inventive concept as the method for calculating the preset values ​​of ballastless track integrating temperature and load in Example 1, this application also provides a system for calculating the preset values ​​of ballastless track integrating temperature and load. Please refer to the appendix. Figure 2 The ballastless track preset value calculation system integrating temperature and load includes: a numerical simulation module 11, used to collect real-time temperature field data and historical train load spectrum data of the target bridge section, construct a coupled mechanical model of ballastless track-bridge structure for numerical simulation, and obtain the simulation estimate of track structure deformation; a data fusion module 12, used to collect measured relative deformation data of track slab and bridge, fuse the simulation estimate of track structure deformation with the measured relative deformation data, and generate a fused dataset; and a constraint inversion module 13, used to perform state estimation based on the fused dataset, generate deformation state values ​​to constrain the ballastless track, perform inversion calculation according to track constraint conditions, and obtain the preset value of ballastless track.

[0072] Furthermore, the numerical simulation module 11 in the ballastless track preset value calculation system integrating temperature and load is also used for: traversing the target bridge section to perform spatial grid analysis, constructing a temperature sensing network for continuous acquisition, and obtaining continuous temperature distribution data; performing three-dimensional spatial analysis based on the continuous temperature distribution data to construct real-time temperature field data; constructing a dynamic update mechanism for the train load spectrum to acquire train operation data in real time for incremental learning and constructing historical train load spectrum data; and performing multi-scale coupling based on the real-time temperature field data and the historical train load spectrum data to construct the ballastless track-bridge structure coupled mechanical model.

[0073] Furthermore, the numerical simulation module 11 in the ballastless track preset value calculation system integrating temperature and load is also used for: mapping the continuous temperature distribution data to a spatial grid to construct a discrete node temperature dataset; extracting multiple spatial coordinates as interpolation base points based on the spatial grid, extracting temperature values ​​based on the multiple spatial coordinates, and using the temperature values ​​as interpolation base values; calculating the interpolation base points for spatial analysis to construct a spatial distance matrix, performing radial analysis on the interpolation base points to construct a radial base value matrix; linearly combining the discrete node temperature dataset based on the interpolation base values ​​and the radial base value matrix to construct a three-dimensional continuous temperature field; and performing heat conduction time delay compensation based on the three-dimensional continuous temperature field to generate the real-time temperature field data.

[0074] Furthermore, the numerical simulation module 11 in the ballastless track preset value calculation system integrating temperature and load is also used for: establishing a multi-scale model hierarchical architecture for analysis, determining the macroscopic scale, mesoscopic scale, and mesoscopic scale; dividing the ballastless track-bridge structure based on the macroscopic scale to determine the bridge structure layer, dividing the ballastless track-bridge structure based on the mesoscopic scale to determine the track structure layer, and dividing the ballastless track-bridge structure based on the mesoscopic scale to determine the interface transition layer; applying coupling constraints based on the multi-scale model hierarchical architecture, setting coupling constraint conditions, the coupling constraint conditions including interface continuity conditions and force balance conditions; coupling the bridge structure layer, the track structure layer, and the interface transition layer according to the interface continuity conditions and the force balance conditions to construct a multi-scale coupled mechanical model; using the real-time temperature field data as a thermodynamic driving input and the historical train load spectrum data as a dynamic driving input to drive the multi-scale coupled mechanical model for verification, thus constructing the ballastless track-bridge structure coupled mechanical model.

[0075] Furthermore, the data fusion module 12 in the ballastless track preset value calculation system that integrates temperature and load is also used for: constructing a multi-source sensing network for the relative deformation of the track slab and the bridge; constructing measured relative deformation data through the measured relative deformation data of the multi-source sensing network; synchronizing the simulated deformation estimate of the track structure with the measured relative deformation data in time and space to obtain spatiotemporally aligned data; dynamically weighting and fusing the simulated deformation estimate of the track structure with the measured relative deformation data according to the spatiotemporally aligned data to generate a weighted dataset; performing data confidence analysis based on the weighted dataset to obtain multiple real-time confidence features; and dynamically adjusting the fusion weights of the weighted dataset based on the multiple real-time confidence features to generate the fused dataset.

[0076] Furthermore, the data fusion module 12 in the ballastless track preset value calculation system integrating temperature and load is also used for: extracting the sampling time data of the measured relative deformation data and extracting the output time data of the track structure deformation simulation prediction; matching the sampling time data and the output time data based on the time dimension to construct a target time reference; performing continuous processing on the measured relative deformation data according to the target time reference to generate a first data processing result; performing data interpolation on the track structure deformation simulation prediction according to the target time reference to generate a second data processing result; performing time synchronization based on the first data processing result and the second data processing result to construct a time synchronization sequence; extracting the finite element mesh node coordinates of the track structure deformation simulation prediction and extracting the sensor data coordinates of the measured relative deformation data; mapping the finite element network node coordinates to the sensor data coordinates based on the spatial dimension to construct a spatial synchronization mapping relationship; and combining the time synchronization sequence and the spatial synchronization mapping relationship to generate the spatiotemporal aligned data.

[0077] Furthermore, the constraint inversion module 13 in the ballastless track preset value calculation system integrating temperature and load is also used for: performing nonlinear state estimation based on the fused dataset to generate deformation state values; performing nonlinear constraint optimization according to the deformation state values ​​to construct track constraint conditions to constrain the ballastless track and determine adjustable spatial constraint information; performing multi-objective optimization based on the adjustable spatial constraint information to generate multiple optimization parameters; and performing inversion solution based on the multiple optimization parameters to determine multiple preset value combinations for screening and generating ballastless track preset values.

[0078] Furthermore, the constraint inversion module 13 in the ballastless track preset value calculation system integrating temperature and load is also used for: performing nonlinear analysis of structural deformation of the ballastless track based on the fused dataset, constructing a nonlinear state transition analysis channel and a nonlinear observation analysis channel; performing an unscented transformation on the fused dataset to determine multiple target sampling points, synchronizing the multiple target sampling points to the nonlinear state transition analysis channel for propagation, and generating a first state transition prediction value; synchronizing the multiple target sampling points to the nonlinear observation analysis channel for propagation, and generating a second observation prediction value; performing uncertainty analysis based on the first state transition prediction value and the second observation prediction value, and constructing an uncertainty covariance matrix; and correcting the first state transition prediction value and the second observation prediction value according to the fused dataset and the uncertainty covariance matrix, thereby generating the deformation state value.

[0079] Furthermore, the constraint inversion module 13 in the ballastless track preset value calculation system integrating temperature and load is also used for: performing track smoothness constraint analysis based on the deformation state value to construct track smoothness constraint conditions; performing track structural force analysis based on the deformation state value to construct structural mechanics feasible domain constraint conditions; performing construction feasibility analysis based on the deformation state value to construct construction feasibility constraint conditions; and coupling the track smoothness constraint conditions, the structural mechanics feasible domain constraint conditions, and the construction feasibility constraint conditions to generate the adjustable spatial constraint information.

[0080] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The calculation method and specific examples of the preset values ​​of ballastless track for fusion temperature and load in the aforementioned embodiment one are also applicable to the calculation system of preset values ​​of ballastless track for fusion temperature and load in this embodiment. Through the foregoing detailed description of the calculation method of preset values ​​of ballastless track for fusion temperature and load, those skilled in the art can clearly understand the calculation system of preset values ​​of ballastless track for fusion temperature and load in this embodiment. Therefore, for the sake of brevity, it will not be described in detail here.

[0081] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0082] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of this application and its equivalents, this application also intends to include such modifications and variations.

Claims

1. A method for calculating preset values ​​of ballastless track integrating temperature and load, characterized in that, The method includes: Real-time temperature field data and historical train load spectrum data of the target bridge section were collected to construct a coupled mechanical model of ballastless track-bridge structure for numerical simulation and obtain the simulation estimate of track structure deformation. Collect measured relative deformation data between the track slab and the bridge, and fuse the predicted deformation value of the track structure with the measured relative deformation data to generate a fused dataset; Based on the fused dataset, state estimation is performed to generate deformable state values ​​to constrain the ballastless track. Inversion calculations are then performed according to the track constraint conditions to obtain the preset values ​​for the ballastless track.

2. The method for calculating the preset values ​​of ballastless track integrating temperature and load as described in claim 1, characterized in that, Real-time temperature field data and historical train load spectrum data of the target bridge section are collected. A coupled mechanical model of ballastless track and bridge structure is constructed for numerical simulation to obtain the simulation estimate of track structure deformation. The methods include: Spatial grid analysis is performed on the target bridge section, and a temperature sensing network is constructed for continuous data acquisition to obtain continuous temperature distribution data. Three-dimensional spatial analysis is performed based on the continuous temperature distribution data to construct real-time temperature field data. A dynamic update mechanism for train load spectrum is constructed to acquire train operation data in real time for incremental learning and to build historical train load spectrum data. Based on the real-time temperature field data and the historical train load spectrum data, a multi-scale coupling was performed to construct the ballastless track-bridge structure coupled mechanical model.

3. The method for calculating the preset values ​​of ballastless track integrating temperature and load as described in claim 2, characterized in that, Based on the continuous temperature distribution data, three-dimensional spatial analysis is performed to construct real-time temperature field data. The method includes: The continuous temperature distribution data is mapped to a spatial grid to construct a discrete node temperature dataset. Multiple spatial coordinates are extracted based on a spatial grid as interpolation base points, and temperature values ​​are extracted based on these multiple spatial coordinates, with the temperature values ​​used as interpolation base values. Calculate the interpolation base points and perform spatial analysis to construct a spatial distance matrix; perform radial analysis on the interpolation base points and construct a radial base value matrix. Based on the interpolation base value and the radial base value matrix, a three-dimensional continuous temperature field is constructed by linearly combining the discrete node temperature dataset. The real-time temperature field data is generated by performing heat conduction time delay compensation based on the three-dimensional continuous temperature field.

4. The method for calculating the preset values ​​of ballastless track integrating temperature and load as described in claim 1, characterized in that, Based on the real-time temperature field data and the historical train load spectrum data, a multi-scale coupling is performed to construct the coupled mechanical model of the ballastless track-bridge structure. The method includes: A multi-scale model with a hierarchical architecture was established for analysis to determine the macroscopic, mesoscopic, and scales. The ballastless track-bridge structure is divided based on the macroscopic scale to determine the bridge structure layer; the ballastless track-bridge structure is divided based on the mesoscopic scale to determine the track structure layer; and the ballastless track-bridge structure is divided based on the mesoscopic scale to determine the interface transition layer. Coupling constraints are implemented based on a multi-scale model hierarchical architecture, and coupling constraint conditions are set, including interface continuity conditions and force balance conditions. According to the interface continuity condition and the force balance condition, the bridge structure layer, the track structure layer, and the interface transition layer are coupled with degrees of freedom to construct a multi-scale coupled mechanical model; The real-time temperature field data is used as the thermal driving input, and the historical train load spectrum data is used as the dynamic driving input to drive the multi-scale coupled mechanical model for verification, thereby constructing the ballastless track-bridge structure coupled mechanical model.

5. The method for calculating the preset values ​​of ballastless track integrating temperature and load as described in claim 1, characterized in that, Collect measured relative deformation data between the track slab and the bridge, and fuse the simulated deformation estimate of the track structure with the measured relative deformation data to generate a fused dataset. The method includes: A multi-source sensing network for the relative deformation of the track slab and the bridge is constructed, and measured relative deformation data is constructed using the relative deformation data measured by the multi-source sensing network; The simulation estimate of the track structure deformation is spatiotemporally synchronized with the measured relative deformation data to obtain spatiotemporally aligned data. The simulation estimate of the track structure deformation and the measured relative deformation data are dynamically weighted and fused according to the spatiotemporal alignment data to generate a weighted dataset. Data confidence analysis is performed on the weighted dataset to obtain multiple real-time confidence features; The fusion weights are dynamically adjusted based on the multiple real-time confidence features to generate the fused dataset.

6. The method for calculating the preset values ​​of ballastless track based on the fusion temperature and load as described in claim 5, characterized in that, The method for spatiotemporally synchronizing the simulated deformation estimate of the track structure with the measured relative deformation data to obtain spatiotemporally aligned data includes: Extract the sampling time data of the measured relative deformation data, and extract the output time data of the simulation prediction of track structure deformation; Based on the time dimension, the sampled time data is matched with the output time data to construct a target time benchmark; The measured relative deformation data is processed continuously according to the target time reference to generate a first data processing result. The simulation estimate of the track structure deformation is interpolated according to the target time reference to generate a second data processing result. Based on the first data processing result and the second data processing result, a time synchronization sequence is constructed. Extract the finite element mesh node coordinates of the predicted deformation value of the track structure from the simulation, and extract the sensor data coordinates of the measured relative deformation data; Based on the spatial dimension, the coordinates of finite element network nodes are mapped to the coordinates of sensor data to construct a spatial synchronous mapping relationship; The time synchronization sequence is combined with the spatial synchronization mapping relationship to generate the spatiotemporal aligned data.

7. The method for calculating the preset values ​​of ballastless track integrating temperature and load as described in claim 1, characterized in that, Based on the fused dataset, state estimation is performed to generate the deformable state values ​​to constrain the ballastless track. Inversion calculations are then performed according to the track constraint conditions to obtain the preset values ​​for the ballastless track. The method includes: Nonlinear state estimation is performed based on the fused dataset to generate deformable state values; Nonlinear constraint optimization is performed based on the deformation state values ​​to construct track constraint conditions for the ballastless track and determine adjustable spatial constraint information; Multi-objective optimization is performed based on the adjustable spatial constraint information to generate multiple optimization parameters; Based on the multiple optimization parameters, an inversion solution is performed to determine multiple preset value combinations, which are then filtered to generate preset values ​​for ballastless track.

8. The method for calculating the preset values ​​of ballastless track integrating temperature and load as described in claim 7, characterized in that, Based on the fused dataset, nonlinear state estimation is performed to generate deformable state values. The method includes: Based on the fused dataset, nonlinear analysis of structural deformation of ballastless track is performed, and nonlinear state transition analysis channel and nonlinear observation analysis channel are constructed. The fused dataset is subjected to an unscented transformation to determine multiple target sampling points. These multiple target sampling points are then synchronized to the nonlinear state transition analysis channel for propagation, generating a first state transition prediction value. The multiple target sampling points are synchronized to the nonlinear observation and analysis channel for propagation to generate a second observation prediction value; Uncertainty analysis is performed based on the first state transition prediction value and the second observation prediction value to construct an uncertainty covariance matrix; The first state transition prediction value and the second observation prediction value are corrected according to the fused dataset and the uncertainty covariance matrix to generate the deformed state value.

9. The method for calculating the preset values ​​of ballastless track integrating temperature and load as described in claim 7, characterized in that, Based on the aforementioned deformation state values, nonlinear constraint optimization is performed to construct track constraint conditions for the ballastless track, and adjustable spatial constraint information is determined. The method includes: Based on the deformation state values, track smoothness constraint analysis is performed to construct track smoothness constraint conditions; Based on the deformation state values, track structure force analysis is performed, and structural mechanics feasible domain constraints are constructed. Based on the deformation state values, a construction feasibility analysis is conducted, and construction feasibility constraints are constructed. The track smoothness constraint, the structural mechanics feasible domain constraint, and the construction feasibility constraint are coupled to generate the adjustable spatial constraint information.

10. A ballastless track preset value calculation system integrating temperature and load, characterized in that, The steps for implementing the method for calculating the preset values ​​of ballastless track for fusion temperature and load according to any one of claims 1 to 9, wherein the system for calculating the preset values ​​of ballastless track for fusion temperature and load comprises: The numerical simulation module is used to collect real-time temperature field data and historical train load spectrum data of the target bridge section, construct a coupled mechanical model of ballastless track-bridge structure for numerical simulation, and obtain the simulation estimate of track structure deformation. The data fusion module is used to collect measured relative deformation data between the track slab and the bridge, and to fuse the simulated deformation estimate of the track structure with the measured relative deformation data to generate a fused dataset. The constraint inversion module is used to perform state estimation based on the fused dataset, generate deformation state values ​​to constrain the ballastless track, and perform inversion calculations according to the track constraint conditions to obtain the preset value of the ballastless track.

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