Railway full-line line base settlement early warning monitoring system based on digital twinning

Abstract

The present application belongs to the technical field of computer aided engineering design and digital twin data processing, and specifically relates to a railway full-line line base settlement early warning monitoring system based on digital twin. The system constructs a settlement propagation diagram according to the continuous relationship of railway mileage, maps the line base section to a twin node and establishes a directed state associated edge, generates a time series residual, a propagation consistency residual and a multi-scale trend residual according to the measured settlement sequence and the twin prediction sequence, inverts an abnormal source and an influence subgraph along the propagation direction, adjusts the node boundary according to the residual aggregation form, and updates the propagation parameters and the state evolution parameters in the influence subgraph. The scheme makes the spatial granularity, parameter sharing boundary and calibration range of the twin model change with the settlement propagation state, reduces the dilution of local anomalies by stable data and the diffusion of calibration errors to the whole line, and realizes continuous monitoring, anomaly positioning and local incremental calibration of the line base settlement.

Description

Technical Field

[0001] This invention belongs to the field of computer-aided engineering design and digital twin data processing technology, specifically a railway subgrade settlement early warning and monitoring system based on digital twins. Background Technology

[0002] Railway subgrade settlement monitoring typically relies on settlement observation data deployed along the line, line mileage information, historical maintenance records, and existing engineering data. The entire line is divided into several monitoring sections according to a preset mileage length, and settlement time series are established for each section. Existing digital twin schemes generally correspond each monitoring section to a virtual subgrade unit, storing the section location, historical settlement, current settlement, settlement change rate, and predicted status in virtual space. New observation data is received at fixed intervals to update the status of the virtual subgrade unit through overlay or recursive updates. For the correlation between adjacent sections, a common practice is to establish fixed connections based on geographical proximity and use the average settlement, change trend, or correlation coefficient of adjacent sections to describe spatial influence. When the data of a certain section changes, the system synchronously corrects the prediction results of adjacent sections according to the established correlation. Such schemes can form a digital state mapping of the entire railway line, but the division boundaries, parameter sharing range, and spatial correlation of twin units are usually determined in the model establishment stage, and are rarely adjusted according to local settlement evolution characteristics during subsequent operation.

[0003] In terms of settlement data processing, existing technologies typically use the difference between measured settlement values ​​and digital twin predicted values ​​as model errors, and correct abnormal and missing data through moving averages, trend fitting, or neighbor interpolation. For continuous mileage sections, the system can calculate spatial smoothing values ​​based on the observation results of adjacent sections, or infer the settlement state at missing times based on historical time series, and then write the corrected data into the digital twin model. Some schemes also calculate short-term settlement changes and long-term settlement trends separately, and mark the corresponding sections as abnormal sections when the difference exceeds a preset range. Since this type of processing mainly focuses on smoothing data for a single section or fixed neighborhood, measured anomalies, data mismatches, and model drift are often uniformly reflected as numerical deviations. It is difficult for the system to determine the source of deviations based on the order of expansion, duration, and multi-timescale changes of the deviations in the mileage direction. The smoothed or interpolated data may also change the original settlement propagation pattern, causing local mutations to be weakened by nearby stable data, or causing single-point errors to expand outward along the fixed neighborhood.

[0004] In terms of digital twin model calibration, existing technologies mostly adopt periodic overall training or independent calibration of sections, recalculating model parameters based on the accumulated measured data within a certain period. Overall training usually inputs data from the entire line into the model and updates the state evolution parameters of each section through a unified objective function. Independent calibration of sections updates local parameters according to predetermined section boundaries and corrects the prediction curves at the section boundaries using mean connection or continuity constraints. To maintain model stability, some schemes set the same parameters or share some parameters for adjacent sections and regenerate the overall settlement prediction results after calibration. Early warning judgments are generally based on the settlement amount, rate of change, or prediction deviation after calibration. The above methods lack a mechanism to limit the calibration range in reverse by the range of abnormal influence. When a local section experiences a sudden change in state, overall training may simultaneously change the parameters of a large number of stable sections, while independent calibration of sections may be restricted by fixed boundaries and cut off the actual propagation relationship. Moreover, it is difficult to retain the correspondence between node splitting, node merging, and parameter inheritance after the model is updated.

[0005] The subgrade settlement of the entire railway line exhibits significant spatial continuity and local abrupt changes. However, fixed mileage zoning, fixed parameter sharing boundaries, and calibration methods oriented towards the entire line or predetermined zones cannot ensure that the spatial granularity and update range of the digital twin model change with the actual settlement propagation state. After a local settlement anomaly occurs, the deviation between the measured and predicted values ​​may originate from abrupt changes in the actual state, data mismatch, or model drift. Existing methods cannot invert the anomaly source and the actual impact range based on the propagation direction, spatial gradient, duration, and multi-scale trend differences of the deviation. This leads to local anomalies being diluted by stable data in excessively large twin units, or calibration errors propagating across the actual impact boundary to stable sections. The core problem thus arises is that the digital twin model cannot implement dynamic zoning and local incremental calibration for anomaly sections that are consistent with the actual impact range while maintaining the continuity of the entire line's state. The spatial boundary of the model and the settlement propagation boundary are mismatched for a long time. Summary of the Invention

[0006] The purpose of this invention is to provide a railway subgrade settlement early warning and monitoring system based on digital twins, which can solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] The railway subgrade settlement early warning and monitoring system based on digital twins includes a subgrade settlement propagation map construction module, a composite residual generation module, an anomaly source inversion module, a twin partition reconstruction module, and a local incremental calibration module.

[0009] The track subgrade settlement propagation map construction module maps the settlement state of each track subgrade section to twin nodes with propagation direction according to the continuous relationship of railway mileage, and establishes directed state association edges between adjacent twin nodes.

[0010] The composite residual generation module generates time-series residuals, propagation consistency residuals, and multi-scale trend residuals based on measured settlement sequences and digital twin prediction sequences.

[0011] The anomaly source inversion module determines the anomaly source and its influence subgraph based on the spatial gradient, duration and propagation direction of the three types of residuals.

[0012] The twin partitioning reconstruction module adjusts the partitioning boundary of the twin nodes according to the aggregation pattern of the anomaly source in the influence subgraph;

[0013] The local incremental calibration module updates the propagation parameters and state evolution parameters only for the adjusted influence subgraph, and writes the update results into the digital twin model.

[0014] Preferably, the line subgrade settlement propagation map construction module performs segment alignment on the historical settlement sequence, the current settlement sequence and the digital twin prediction sequence based on unified mileage coordinates, encodes the sequential relationship of settlement changes between adjacent segments as directed state association edges, and establishes an edge state vector composed of propagation time delay, amplitude attenuation and trend similarity for each directed state association edge.

[0015] The subgrade settlement propagation diagram construction module also forms a parameter sharing boundary based on the stability of the edge state vector within the continuous observation window, so that twin nodes located within the same parameter sharing boundary share the basic evolution parameters, and twin nodes crossing the parameter sharing boundary retain independent evolution parameters. When new settlement data arrives, only the directed state-related edge and the corresponding edge state vector associated with the new settlement data are updated.

[0016] Preferably, the composite residual generation module calculates the temporal residual between the measured settlement value and the digital twin predicted value, the propagation consistency residual between the target twin node and its upstream twin node, and the trend difference residual of the same twin node in the short-term window, medium-term window and long-term window, respectively, according to the same time base, and arranges the three types of residuals into residual tensors according to mileage position and time position.

[0017] The anomaly source inversion module performs reverse backtracking on the residual tensor along the directed state association edge of the subgrade settlement propagation diagram. It constructs an anomaly source candidate set based on the directional consistency, scale consistency, and persistence consistency of the residual increment between adjacent twin nodes, and determines the anomaly source location and anomaly source range according to the interpretability coverage of the downstream residuals by the candidate locations.

[0018] Preferably, the twin partition reconstruction module extracts the turning points of the residual spatial gradient within the range of the anomaly source, reconstructs the line base segments between adjacent turning points into candidate twin nodes, and performs splitting or merging based on the trend homogeneity within the candidate twin nodes and the propagation difference between the candidate twin nodes.

[0019] During the splitting process, the twin partition reconstruction module allocates the state history of the original twin node to the split twin node according to the mileage position, and retains the time order of the original state-related edges.

[0020] During the merging process, the twin partition reconstruction module forms a merging state sequence based on the data integrity of each candidate twin node;

[0021] The local incremental calibration module uses the reconstructed node boundary as the calibration boundary and jointly updates the state evolution parameters and directed state association edge parameters within the calibration boundary.

[0022] Preferably, the line subgrade settlement propagation map construction module establishes multiple candidate propagation paths for each directed state-associated edge, maps the state changes of the upstream twin node to the downstream twin node with different propagation time delays, and forms path credibility based on the reconstruction error of each candidate propagation path on the measured settlement changes downstream.

[0023] When the path credibility of multiple candidate propagation paths is close, multiple propagation delays and their weights are retained as the combined propagation state of the directed state associated edges. When the path credibility of a single candidate propagation path continues to dominate, the corresponding propagation delay is solidified into the main propagation state.

[0024] The parameter sharing boundary is adjusted based on the difference in the combined propagation state of adjacent directed state associated edges, and the position where the main propagation state transitions is set as the boundary position where cross-regional sharing of evolution parameters is prohibited.

[0025] Preferably, the anomaly source inversion module performs local state replacement on each candidate position in the anomaly source candidate set, replaces the measured settlement segment corresponding to the candidate position with the digital twin prediction segment, and recalculates the propagation consistency residual and trend difference residual of the downstream twin node along the directed state association edge to obtain the inversion residual reduction map corresponding to the candidate position.

[0026] The anomaly source inversion module sorts candidate locations based on the continuous mileage range of residual reduction, the degree of cross-scale preservation, and the degree of consistency with the propagation direction in the inversion residual reduction map. Candidate locations that can simultaneously reduce temporal residuals, propagation consistency residuals, and trend difference residuals are retained as main anomaly sources, while candidate locations that only reduce local temporal residuals and do not form downstream continuous responses are marked as data mismatch locations.

[0027] Preferably, the twin partition reconstruction module establishes a mapping matrix between the original node state trajectory and the candidate child node state trajectory before splitting the twin node, uses the mapping matrix to generate the initial state sequence of the candidate child nodes respectively, and reconstructs the directed state association edge according to the propagation order relationship between the candidate child nodes and the upstream and downstream twin nodes.

[0028] Before merging twin nodes, the twin partition reconstruction module performs gap alignment on the time axis of the candidate twin nodes, encodes the data integrity, residual stability and propagation consistency at the same time as fusion weights, and uses the fusion weights to generate a merged state sequence.

[0029] After splitting or merging, the node correspondence and parameter inheritance relationship before and after reconstruction are retained to form a twin version mapping table for subsequent incremental calibration.

[0030] Preferably, the local incremental calibration module expands the calibration neighborhood upstream and downstream according to the range of the anomaly source, and the expansion range is determined by the propagation delay and amplitude attenuation of the directed state-related edge, and sets the state and parameters of the twin node outside the calibration neighborhood to a frozen state.

[0031] The local incremental calibration module alternately updates the state evolution parameters of the twin nodes and the propagation parameters of the directed state-related edges within the calibration neighborhood. After each round of updates, the boundary node parameters are adjusted based on the prediction continuity at the boundary of the calibration neighborhood, and a difference index is established between the residual tensors before and after calibration.

[0032] When the difference index indicates that the calibration error is spreading to the frozen region, the current parameter update is revoked and the calibration neighborhood is expanded according to the propagation direction before a joint update is performed again.

[0033] Preferably, the anomaly source inversion module generates anomaly interpretation branches for the main anomaly source and the data mismatch location, respectively. The anomaly interpretation branches include a state change branch that retains the measured settlement segment, a data repair branch that replaces the measured settlement segment with the propagation results of adjacent twin nodes, and a model drift branch that keeps the observation data unchanged and adjusts the digital twin evolution parameters.

[0034] The anomaly source inversion module calculates the residual tensor corresponding to each anomaly interpretation branch, and determines the branch consistency based on the reduction range of downstream continuous residuals and the degree of preservation of upstream stable residuals by the anomaly interpretation branch. The anomaly interpretation branch with the highest branch consistency is written into the anomaly source label, while the remaining anomaly interpretation branches are reserved as candidate branches for re-comparison when new settlement data arrives.

[0035] Preferably, the local incremental calibration module stores the state evolution parameters, directed state-related edge parameters and residual tensors before and after each node reconstruction based on the twin version mapping table, and forms a parameter migration graph for two consecutive calibrations.

[0036] The parameter migration graph uses the pre-reconstruction node, the post-reconstruction node, and the calibration boundary node as vertices, and parameter inheritance, parameter splitting, and parameter fusion as migration edges.

[0037] When new settlement data causes the same anomaly source's influence range to be reconstructed again, the local incremental calibration module searches for historical calibration paths consistent with the current node boundary along the parameter migration graph, uses the parameter changes in the historical calibration paths as the initial constraints for this joint update, and compares the current residual tensor with the historical residual tensor after the update is completed, retaining only the parameter migration paths that do not cause the residual outside the calibration boundary to increase in the opposite direction.

[0038] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0039] 1. By constructing a track subgrade settlement propagation map with propagation direction according to the continuous relationship of railway mileage, and converting the measured settlement sequence and the digital twin prediction sequence into time-series residuals, propagation consistency residuals, and multi-scale trend residuals, the location of deviation generation, propagation direction, and duration range can be described in a unified spatiotemporal correlation structure. The anomaly source inversion process traces back the residual changes along the directed state correlation edge, and determines the anomaly source and its influence sub-map based on spatial gradient, duration, and propagation direction. The twin partition reconstruction process then adjusts the node boundaries based on the anomaly source aggregation pattern and residual turning point, so that the locally complex sections are split into finer twin nodes, and adjacent sections that have maintained stable evolution in the same direction for a long time are kept in a merged state. Local incremental calibration is limited to the reconstructed influence sub-map, and the states and parameters outside the influence sub-map are kept frozen. When the calibration error spreads to the frozen area, the update is canceled and the calibration neighborhood is adjusted. This keeps the model spatial boundary, parameter update boundary, and actual settlement propagation boundary corresponding, reducing the dilution of local anomalies by stable data and the spread of update errors to the entire line.

[0040] 2. Directed state-related edges are formed using propagation delay, amplitude decay, and trend similarity to create edge state vectors. Parameter sharing boundaries are determined based on stability within the continuous observation window, allowing parameter sharing relationships between adjacent segments to change with the propagation state, rather than being constrained by fixed mileage boundaries in the long term. Local state replacement is performed on candidate anomaly source locations, generating inversion residual reduction maps. The main anomaly source and data mismatch locations can be distinguished based on continuous mileage range, cross-scale retention, and consistency of propagation direction. Different anomaly interpretations are preserved through state mutation branches, data repair branches, and model drift branches. During node splitting or merging, a state mapping matrix, fusion weights, and twin version mapping tables are established to save the node correspondence and parameter inheritance relationships before and after reconstruction. The parameter migration map formed by continuous calibration can call historical calibration paths consistent with the current node boundary and exclude migration paths that cause an increase in residuals outside the calibration boundary, maintaining data continuity between multiple reconstructions and calibrations and reducing parameter jumps caused by repeated calibrations. Attached Figure Description

[0041] Figure 1 This is a flowchart illustrating the overall processing flow of a railway subgrade settlement early warning and monitoring system based on digital twins.

[0042] Figure 2 Flowchart for constructing a subgrade settlement propagation map and generating a composite residual tensor;

[0043] Figure 3 A flowchart for anomaly source inversion, influence subgraph determination, and twin partition dynamic reconstruction;

[0044] Figure 4 The flowchart shows the process of local incremental calibration, boundary checking, and parameter migration affecting the subgraph.

[0045] Figure 5 The path reliability curve is shown in the edge state vector diagram.

[0046] Figure 6 This is a trend chart of risk deviation for the composite residual tensor.

[0047] Figure 7 A ranking chart of candidate inversion scores for anomaly sources;

[0048] Figure 8 A graph showing the criteria for splitting and merging twin partitions;

[0049] Figure 9 A comparison chart of the objective functions for local joint calibration. Detailed Implementation

[0050] In one embodiment, please refer to Figure 1A railway subgrade settlement early warning and monitoring system based on digital twins includes a subgrade settlement propagation map construction module, a composite residual generation module, an anomaly source inversion module, a twin partition reconstruction module, and a local incremental calibration module. The subgrade settlement propagation map construction module maps the settlement state of each subgrade section to twin nodes with propagation directions according to the continuous relationship of railway mileage, and establishes directed state association edges between adjacent twin nodes. The composite residual generation module generates temporal residuals, propagation consistency residuals, and multi-scale trend residuals based on measured settlement sequences and digital twin prediction sequences. The anomaly source inversion module determines the anomaly source and its influence subgraph based on the spatial gradient, duration, and propagation direction of the three types of residuals. The twin partition reconstruction module adjusts the partition boundaries of twin nodes according to the aggregation pattern of anomalies within the influence subgraph. The local incremental calibration module updates the propagation parameters and state evolution parameters only for the adjusted influence subgraph and writes the update results into the digital twin model.

[0051] In this embodiment, the line base section does not permanently correspond to a fixed-length twin node. Instead, it uses a unified mileage coordinate as the main index and continuous observation time as the secondary index. The historical settlement sequence, current settlement sequence, predicted settlement sequence, and data integrity identifier within the same mileage range are written into the node status record. The node status record includes at least the observation time, mileage start point, mileage end point, cumulative settlement, changes between adjacent times, short-term trend items, medium-term trend items, long-term trend items, and model version number. The line base settlement propagation map construction module compares the order of changes between adjacent nodes. When the changes of the upstream node can form a consistent response in the downstream node after several observation periods, a directed state association edge from the upstream node to the downstream node is established. When the propagation direction changes over time, bidirectional candidate edges are retained, but their respective propagation states are recorded separately, avoiding processing all sections as undirected connections based solely on spatial adjacency.

[0052] Specifically, the subgrade settlement propagation map construction module writes the new settlement data into the corresponding temporary node cache according to the mileage position after each new settlement data is received. It also performs time alignment of the observation sequence within the same node using timestamps. For data that could not be obtained at the same observation time, it does not directly fill in a uniform interpolation value, but retains the missing marker and its adjacent valid value index. Then, it updates the directed state association edge according to the change direction, change arrival order and change amplitude ratio between the temporary node and the preceding and following nodes, so that the propagation relationship can continuously change with the new data. The composite residual generation module reads the aligned measured settlement sequence and the prediction sequence generated by the current digital twin version, and forms the node internal residual, edge propagation residual and multi-timescale trend residual respectively under the same time reference. It then establishes association between the residual and the corresponding node number, edge number, observation window and model version.

[0053] Furthermore, the anomaly source inversion module does not use a single residual exceeding a fixed value as the anomaly source determination criterion. Instead, it performs a reverse search along the directed state association edge from the residual occurrence segment to the possible upstream segment. Candidate nodes whose residual spatial gradient increases from small to large and can continuously explain the residuals of multiple downstream nodes are retained as anomaly source candidates. Candidate positions that only appear at isolated moments and cannot form a continuous response along the existing propagation direction are retained as data mismatch candidates. Candidate regions that appear simultaneously in multiple adjacent nodes but lack a clear propagation starting point are retained as model drift candidates. Subsequently, the anomaly source and the influence subgraph are determined using the local state replacement and inversion residual reduction results. The influence subgraph consists of the anomaly source node, the downstream node affected by the propagation of the anomaly source, and a small number of upstream nodes required to maintain boundary continuity.

[0054] Preferably, the twin partition reconstruction module only analyzes the residual turning point, trend homogeneity, and propagation difference within the influence subgraph. When there is a continuous residual gradient turning point within the original twin node and the trend direction or propagation time lag on both sides of the turning point is different, the original twin node is split using the turning point as the candidate boundary. When adjacent twin nodes maintain the same trend direction, similar propagation state, and long-term stable boundary residuals within a continuous observation window, the adjacent twin nodes are merged. The local incremental calibration module updates the state evolution parameters and propagation parameters within the reconstructed influence subgraph and freezes the node states and parameters outside the influence subgraph. If a new reverse increase in residuals occurs between the calibrated boundary node and the frozen node, the current update is canceled and the calibration neighborhood is expanded before re-execution, so that the spatial boundary, parameter update boundary, and actual settlement propagation range of the digital twin model remain corresponding.

[0055] In a preferred embodiment, please refer to Figure 2 The line subgrade settlement propagation map construction module aligns historical settlement sequences, current settlement sequences, and digital twin prediction sequences based on unified mileage coordinates. It encodes the sequential relationship of settlement changes between adjacent segments as directed state-related edges and establishes an edge state vector for each directed state-related edge, composed of propagation delay, amplitude attenuation, and trend similarity. The line subgrade settlement propagation map construction module also forms parameter-sharing boundaries based on the stability of the edge state vectors within a continuous observation window. This allows twin nodes located within the same parameter-sharing boundary to share basic evolution parameters, while twin nodes crossing the parameter-sharing boundary retain independent evolution parameters. When new settlement data arrives, only the directed state-related edges associated with the new settlement data and their corresponding edge state vectors are updated.

[0056] The edge state vector can be determined by the following formula:

[0057] ;

[0058] Where a represents a candidate upstream twin node, b represents a candidate downstream twin node, r represents the aligned observation sequence number, and M represents the number of valid observations within the continuous observation window. This indicates that node a is lagging. Settlement changes over one observation period This represents the amount of sedimentation change at node b in the current sequence number. Indicates the amplitude attenuation coefficient. This represents the offset used to absorb local baseline differences. , and These represent the propagation delay, amplitude decay, and offset corresponding to the minimum error, respectively. The trend similarity is determined by the proportion of the fitted sequence and the measured change sequence of node b in the same direction. For example, if the candidate delay is 1, 2, or 3 observation periods, and the square error corresponding to delay 2 is the smallest and the fitted sequence is consistent with the measured change direction for most moments, then 2 is recorded as the current main propagation delay, and the corresponding amplitude decay and trend similarity are written into the edge state vector.

[0059] Please refer to Figure 5 , Figure 5 The horizontal axis represents the state-related edge sequence number arranged in order of route mileage, covering 239 adjacent twin node-related edges; the vertical axis represents path reliability, with a value ranging from approximately 0 to 1.1. Solid lines represent the path reliability of each related edge after candidate propagation delay enumeration and least-squares fitting, dashed lines represent combined propagation retention lines, and dotted lines represent main propagation fixed lines. This diagram corresponds to the edge state vector fitting formula, used to visually present the edge reliability after the combined effects of propagation delay, amplitude attenuation, offset, and trend similarity.

[0060] from Figure 5 As can be seen, the path confidence of most state-related edges is concentrated between 0.45 and 0.60, with an average of approximately 0.523, indicating a relatively stable propagation correlation between settlement changes in adjacent sections along the entire line. However, most edges have not yet reached the main propagation solidification line. The curve near the 123rd related edge shows a significant rise, with a peak value of approximately 0.714, corresponding to the propagation relationship between nodes N123 and N124. Its candidate propagation time lag is one observation period, and the trend similarity is approximately 0.819, indicating that the arrival order and direction of settlement changes in the upstream and downstream areas at this location are highly consistent.

[0061] Figure 5 The confidence level of the path near the 56th associated edge drops to approximately 0.431, below the combined propagation retention line. This indicates that the edge state fitting at this location is highly sensitive to observation noise, local missing values, or boundary state changes, and it is not advisable to directly solidify it as the main propagation path. For such low-confidence edges, multiple candidate propagation delays and their weights should be retained, and the stability of the main propagation state and the combined propagation state should be compared in subsequent continuous observation windows.

[0062] Figure 5 The overall trend also shows that confidence levels exhibit local spikes and short-distance fluctuations near high-risk areas, which are related to boundary locking, bidirectional combined propagation states, and local subsidence anomaly propagation. If the confidence level in a continuous segment remains higher than the retention line but does not stably exceed the solidification line, the combined propagation state should be used to confirm the influence subgraph. If subsequent observations result in the highest confidence level consistently dominating, this edge can be converted into the main propagation edge, and it can be allowed to participate in the propagation direction expansion of neighborhood calibration.

[0063] therefore, Figure 5 This provides a visual explanation of the edge state vector formula in the main text, demonstrating that the propagation delay is not a single fixed quantity, but rather a dynamic edge state result formed under the joint constraints of candidate delay, amplitude attenuation, offset, and trend similarity. This result can serve as the basic input for directed propagation graph construction, parameter-sharing boundary judgment, reverse candidate edge retention, and local calibration neighborhood expansion.

[0064] The formation of parameter sharing boundaries is based on the continuous stability of edge state vectors. After each observation window, the subgrade settlement propagation map construction module compares the propagation time delay changes, amplitude attenuation changes, and trend similarity changes of adjacent directed state-related edges. When the edge state vectors between multiple consecutive nodes maintain the same direction of change in the previous and subsequent observation windows and no main propagation time delay transition occurs, these nodes are assigned to the same parameter sharing region and share the basic evolution parameters. When the main propagation time delay of a certain side undergoes a continuous transition or the trend similarity changes from the same direction to the opposite direction, the mileage position of that side is set as the parameter sharing boundary. The nodes on both sides of the boundary save independent evolution parameters. After the arrival of new settlement data, only the edge state vectors directly related to the new data are re-estimated and the boundary is checked along the adjacent edges to see if it needs to be moved, thus avoiding repeated calculations of the entire map.

[0065] Furthermore, the line subgrade settlement propagation map construction module establishes multiple candidate propagation paths for each directed state-related edge, maps the state changes of the upstream twin node to the downstream twin node with different propagation time delays, and forms path credibility based on the reconstruction error of each candidate propagation path on the measured settlement changes downstream; when the path credibility corresponding to multiple candidate propagation paths is close, multiple propagation time delays and their weights are retained as the combined propagation state of the directed state-related edge; when the path credibility of a single candidate propagation path is consistently dominant, the corresponding propagation time delay is solidified into the main propagation state; the parameter sharing boundary is adjusted according to the difference in the combined propagation state of adjacent directed state-related edges, and the position where the main propagation state transitions is set as the boundary position where cross-regional sharing of evolution parameters is prohibited.

[0066] The generation of candidate propagation paths does not employ arbitrary expansion methods. Instead, it uses the upstream neighboring nodes of the current node and nodes with historically stable propagation relationships as candidate sources. Propagation paths are generated separately within the allowable observation lag range, and the reconstruction error corresponding to each path is converted into a normalized confidence level. If the difference between the highest confidence level and the second highest confidence level does not reach the preset stability criterion, multiple corresponding propagation lags are retained and the results are normalized according to the confidence level to form a combined propagation state. Subsequent residual calculations propagate along multiple paths simultaneously and synthesize edge propagation predictions according to weights. If the same propagation lag maintains the highest confidence level in multiple consecutive observation windows and its reconstruction error does not show directional shift, it is solidified into the main propagation state. When the main propagation state changes, the parameter sharing boundary is checked synchronously, so that boundary adjustment is triggered by changes in the propagation mechanism rather than by single residual fluctuations.

[0067] In this embodiment, please refer to Figure 3 The composite residual generation module calculates the temporal residual between the measured settlement value and the digital twin predicted value, the propagation consistency residual between the target twin node and its upstream twin node, and the trend difference residual of the same twin node in the short-term, medium-term, and long-term windows, respectively, according to the same time base. The three types of residuals are arranged into residual tensors according to mileage and time position. The anomaly source inversion module performs reverse backtracking on the residual tensor along the directed state correlation edge of the line subgrade settlement propagation map. Based on the directional consistency, scale consistency, and persistence consistency of the residual increment between adjacent twin nodes, it constructs an anomaly source candidate set and determines the anomaly source location and anomaly source action range according to the interpretability coverage of the downstream residuals by the candidate location.

[0068] The residual tensor can be constructed using the following formula:

[0069] ;

[0070] Where p represents the twin node position sorted by mileage, q represents the observation position under a unified time base, and s represents the short-term window, medium-term window, or long-term window. This represents the measured settlement value. Represents the predicted value of the digital twin. This represents the propagation prediction value obtained based on the upstream node and the directed state-related edges. This represents the trend of the measured sequence at scale s. This represents the trend of the predicted sequence at the same scale. , and The three terms, with a sum of 1, are non-negative weights. They correspond to the time-series residual, the propagation consistency residual, and the trend difference residual, respectively. For example, when the measured value of a node is close to the twin prediction value but deviates from the upstream propagation prediction value and the medium- and long-term trend direction is consistent, the second term makes the main contribution. Based on this, the anomaly source inversion module prioritizes checking the propagation relationship without directly changing the node's own evolution parameters.

[0071] Please refer to Figure 6 , Figure 6 The horizontal axis represents the residual calculation records sorted by mileage and time sequence within the unified observation window, and the vertical axis represents the composite residual intensity, in millimeters. The curves correspond to the composite residual tensor calculation results under the medium-term observation window, with dashed lines and dotted lines representing the first-level and second-level warning thresholds, respectively. This figure corresponds to the composite residual formula, where the temporal residual, propagation consistency residual, and multi-scale trend difference residual are combined into the total residual after weight normalization.

[0072] from Figure 6 As can be seen, the overall residual level of the 420 valid calculation records currently displayed is low, with an average composite residual of approximately 0.873 mm, far below the first-level warning threshold of 6 mm and the second-level warning threshold of 12 mm. This indicates that within the current model version and observation window, the measured settlement, twin predictions, and propagation predictions for most mileage nodes are consistent. The initial segment of the curve exhibits low-amplitude stable fluctuations, reflecting the normal deviation between settlement predictions and observed values ​​under normal operating conditions.

[0073] Figure 6 A residual increase occurred in the later part of the range, with a maximum value of approximately 1.406 mm, corresponding to the mid-term window calculation record of node N238 on July 15, 2026. Although this peak value did not reach the warning threshold, the contribution of propagation consistency residuals to its sub-contributions was approximately 94.3%, significantly higher than that of time-series residuals and trend difference residuals. This indicates that the deviation at this point mainly stemmed from the inconsistency between upstream propagation predictions and current measured settlement, rather than simply from the node's own prediction errors.

[0074] The minimum local trough of the curve is approximately 0.009 mm, occurring at an earlier observation time at the same node, indicating that this node can be fully explained by the model and propagation relationship within a certain time window. The variation of high and low residuals at different time periods at the same node demonstrates that the composite residual tensor can reflect the evolution of settlement risk over observation time, rather than making a static judgment only at a fixed mileage location.

[0075] therefore, Figure 6This provides a graphical verification of the composite residual tensor formula in the main text. By simultaneously displaying the residual strength, threshold position, and continuous curve changes, it supports subsequent anomaly source inversion, influence subgraph confirmation, and local calibration neighborhood delineation. When the residuals of consecutive mileage nodes gradually increase and the propagation consistency term dominates, the directed edge propagation relationship should be checked first; when the time-series residuals dominate and do not form downstream continuous reduction, it is more likely to enter the data repair branch.

[0076] The short-term, medium-term, and long-term windows employ nested time ranges. The short-term window preserves rapidly changing directional information, the medium-term window determines whether changes persist across multiple observation periods, and the long-term window identifies baseline drift and slow accumulation trends. The composite residual generation module performs missing location masking and effective observation normalization for each window to prevent differences in the number of missing data from directly altering the magnitude of the trend residual. When short-term residuals are prominent while medium- and long-term residuals remain stable, the corresponding location is marked as a candidate for instantaneous change. When short-term and medium-term residuals continuously expand along the mileage direction and long-term residuals begin to change in the same direction, the corresponding region is marked as a candidate for continuous propagation. When all three scales change synchronously in multiple adjacent nodes without a clear propagation order, the corresponding region is marked as a candidate for model drift. The marking results are used as search constraints for reverse backtracking of anomaly sources.

[0077] The anomaly source backtracking starts from the target node in the residual tensor that exceeds the local baseline. It visits upstream nodes in the direction of propagation along the directed state association edges. For each upstream node visited, the occurrence time of the residual, the direction of residual increment, and the cross-scale consistency between the current node and the upstream node are compared. If the occurrence time of the residual of the upstream node is earlier than that of the current node and the increment direction of the two are consistent, the backtracking continues upstream. If the occurrence time is the same but the propagation consistency residual has not increased, it is retained as a concurrent candidate. If the occurrence time of the residual of the upstream node is later or the direction is opposite, the current path is stopped. When multiple backtracking paths converge at the same candidate node, the anomaly source inversion module counts the number of downstream consecutive nodes that the candidate node can explain, the time span that can be explained, and the number of residual types that can be explained, and forms an anomaly source candidate set based on this.

[0078] In a preferred embodiment, the anomaly source inversion module performs local state replacement on each candidate location in the anomaly source candidate set, replacing the measured settlement segment corresponding to the candidate location with the digital twin prediction segment, and recalculates the propagation consistency residual and trend difference residual of the downstream twin node along the directed state association edge to obtain the inversion residual reduction map corresponding to the candidate location; the anomaly source inversion module sorts the candidate locations according to the continuous mileage range of residual reduction, the degree of cross-scale preservation, and the degree of consistency with the propagation direction in the inversion residual reduction map, and retains the candidate locations that can simultaneously reduce the temporal residual, the propagation consistency residual, and the trend difference residual as the main anomaly source, and marks the candidate locations that only reduce the local temporal residual and do not form a downstream continuous response as data mismatch locations.

[0079] The inversion score for a candidate position can be calculated using the following formula:

[0080] ;

[0081] Where c represents the candidate position of the anomaly source. This represents the mileage range within which the downstream residual is continuously reduced after a partial state replacement is performed. This indicates the total mileage range of the currently searched subgraph. This indicates the number of scales at which residual reduction is maintained across short-term, medium-term, and long-term scales. This represents the total number of scales involved in the calculation. This represents the number of residual reduction edges that propagate in the same direction as the edges associated with the directed state. This indicates the number of valid edges downstream of the candidate position. This indicates the number of new residuals added in the upstream stable region after the replacement. This indicates the number of valid comparisons in the upstream stable region. to For example, a candidate position can achieve a higher inversion score when it can simultaneously reduce the residuals of three scales over a long downstream mileage range without increasing the upstream residuals, while a candidate position that only reduces the time series residuals of this node can achieve a lower inversion score and enter the data mismatch candidate set.

[0082] Please refer to Figure 7 , Figure 7 The horizontal axis represents the candidate anomaly source ranking number, and the vertical axis represents the candidate inversion score, ranging from 0 to 1.2. The solid line represents the comprehensive score calculated for each candidate location based on the downstream residual continuous reduction mileage, the number of cross-scale maintained values, the number of edges with consistent propagation direction, and the number of newly added residuals in the upstream stable region. The dashed line represents the review judgment line, and the dotted line represents the main source judgment line. This figure corresponds to the anomaly source candidate inversion score formula and is used to demonstrate the differences in the ability of candidate sources to explain downstream residuals.

[0083] from Figure 7 As can be seen, the candidate position ranked first has a score of approximately 0.756, significantly higher than the main source determination line of 0.68, corresponding to the section from K61+000 to K61+500. After local state replacement, this candidate position can generate approximately 7.5 km of continuous downstream residual reduction, maintaining reduction across short-term, medium-term, and long-term scales, with 12 downstream edges aligned with the propagation direction. Meanwhile, no new residuals are added in the upstream stable region. Therefore, its score is jointly increased by the reduction mileage term, the cross-scale term, and the propagation direction alignment term.

[0084] The scores of candidate positions ranked lower gradually decrease, with the lowest candidate score being approximately 0.167, corresponding to the K87+000 to K87+500 segment. This candidate only forms a downstream reduction range of about 1.2km, and the number of edges maintaining consistency in quantity and direction across scales is relatively small. Although the penalty for newly added upstream residuals is not significant, it is difficult to explain the continuous propagation of residuals overall. Therefore, it is more suitable as a data mismatch location or a candidate to be reviewed, rather than being directly included in the main anomaly source label.

[0085] Figure 7 The candidate scores decrease rapidly from the first to subsequent positions, indicating that there is a relatively clear main anomaly source explanation path within the current influencing subplot. If multiple candidate scores are close and all are near the review decision line, the candidate set should be retained, awaiting further differentiation based on new observations or joint replacement results. However, in this figure, the difference between the first candidate and the low-scoring candidates is significant, indicating that simply replacing the position of this candidate can explain a large range of downstream residual reduction.

[0086] therefore, Figure 7 This is a visual explanation of the anomaly source inversion formula in the main text. Its engineering significance lies in transforming multiple anomaly interpretation branches into a sortable candidate set, and jointly determining the main anomaly source, data mismatch location, and model drift candidate through downstream continuous reduction, cross-scale consistency, propagation direction consistency, and upstream stability maintenance, providing quantitative basis for subsequent label confirmation, candidate retention, or transfer to work order processing.

[0087] Local state replacement only changes the temporary copy used for inversion calculation and does not directly overwrite the measured data. The anomaly source inversion module establishes an independent copy for each candidate location, replaces the measured settlement segment within the candidate time slice with the predicted segment generated by the same digital twin version, and keeps other nodes and other time slices unchanged. Then, it recalculates the propagation prediction and multi-scale trend along the original state association edge and compares the difference in residual tensors before and after replacement. If the multiple types of residuals in the downstream continuous segment decrease together after replacing a candidate location and no new residuals are generated in the upstream stable segment, then the candidate location has source interpretation capability. If only the residual of this node decreases while the downstream residuals remain unchanged, then the corresponding data is more likely to be a local mismatch. If multiple adjacent candidate locations cannot form a clear directional reduction after replacement, then the model drift candidate is retained and the comparison is moved to the anomaly interpretation branch.

[0088] Furthermore, the anomaly source inversion module generates anomaly interpretation branches for the main anomaly source and the data mismatch location, respectively. The anomaly interpretation branches include a state change branch that retains the measured settlement segment, a data repair branch that replaces the measured settlement segment with the propagation results of adjacent twin nodes, and a model drift branch that keeps the observed data unchanged and adjusts the digital twin evolution parameters. The anomaly source inversion module calculates the residual tensor corresponding to each anomaly interpretation branch, and determines the branch consistency based on the reduction range of the downstream continuous residual and the degree of preservation of the upstream stable residual. The anomaly interpretation branch with the highest branch consistency is written into the anomaly source label, while the remaining anomaly interpretation branches are reserved as candidate branches for re-comparison when new settlement data arrives.

[0089] The state mutation branch directly retains the measured settlement segment and allows subsequent partition reconstruction to adjust the node boundaries around this segment. The data repair branch selects the propagation results from adjacent nodes with stable propagation relationships in the upstream and downstream that can jointly explain the trend of the current segment, and synthesizes replacement segments according to the credibility of the edge state vector. The model drift branch keeps all observation data unchanged and only adjusts the node evolution parameters and propagation parameters in a temporary copy of the influence subgraph. The three branches generate new residual tensors respectively. The anomaly source inversion module compares the downstream continuous residual reduction range, the upstream stable residual maintenance, and cross-scale consistency. The branch with the highest consistency is written with the anomaly source label. The other branches are not deleted, but the corresponding data replacement range, parameter adjustment range, and residual changes are recorded. When new data arrives, the same observation window is used to re-compare to avoid a single observation permanently fixing the anomaly properties.

[0090] In this embodiment, the twin partition reconstruction module extracts the turning points of the residual spatial gradient within the anomaly source's influence range, reconstructs the line base segments between adjacent turning points into candidate twin nodes, and performs splitting or merging based on the trend homogeneity within the candidate twin nodes and the propagation differences between them. During splitting, the twin partition reconstruction module allocates the state history of the original twin node to the split twin nodes according to their mileage location, while preserving the temporal order of the original directed state-related edges. During merging, the twin partition reconstruction module forms a merged state sequence based on the data completeness of each candidate twin node. The local incremental calibration module uses the reconstructed node boundary as the calibration boundary and jointly updates the state evolution parameters and directed state-related edge parameters within the calibration boundary.

[0091] The residual spatial gradient is calculated based on the difference in residual tensors between adjacent mileage locations, and directional consistency is checked at multiple consecutive observation times. Candidate boundaries are formed only when there are repeated transitions from low residual regions to high residual regions or from high residual regions to low residual regions near the same mileage location. The twin partition reconstruction module obtains multiple candidate twin nodes by separating them with the candidate boundaries. Then, it calculates the dispersion of short-term, medium-term, and long-term trends within each candidate twin node, as well as the differences in propagation delay, amplitude decay, and trend similarity between adjacent candidate twin nodes. Regions with inconsistent trends within nodes and different propagation states on both sides of the boundary are split, while regions with consistent trends within nodes and similar adjacent propagation states are merged, so that partition changes are jointly determined by the residual structure and the propagation structure.

[0092] The criteria for splitting or merging can be constructed as follows:

[0093] ;

[0094] Where d represents the candidate boundary, This indicates the degree of stability transition of the residual spatial gradient on both sides of the candidate boundary. This indicates the difference in multi-scale trends on both sides of the candidate boundary. This represents the difference in state vectors between the two sides of the candidate boundary. This indicates the degree of trend homogeneity within the merged nodes after removing candidate boundaries. to They are respectively represented as , , and The corresponding non-negative coefficients sum to 1, when Maintaining positive values ​​and preserving candidate boundaries while remaining stable within a continuous observation window, and performing splitting, when When the value remains negative and there is no transition between the main propagation states on both sides, the candidate boundary is removed and the merging is performed. For example, when the residuals show a clear turning point, the trend directions are different, and the propagation delays change, the first three terms increase together, and the candidate boundary is retained. However, when the trends on both sides are consistent, the propagation states are similar, and the internal homogeneity is high after merging, the fourth term dominates, and the candidate boundary is removed.

[0095] Please refer to Figure 8 , Figure 8 The horizontal axis represents the candidate boundary numbers extracted in mileage order, and the vertical axis represents the partition boundary criterion score. Solid lines represent the comprehensive score calculated based on the degree of stability transition of the residual space gradient, multi-scale trend differences, edge state vector differences, and the homogeneity of trends after merging for each candidate boundary. Dashed lines represent removed boundary lines, and dotted lines represent retained boundary lines. This figure corresponds to the twin partition splitting and merging criterion formula, used to determine whether candidate boundaries should be retained, split, or merged.

[0096] from Figure 8 As can be seen, the criterion scores of the 80 candidate boundaries generally fluctuate around zero, with an average of approximately -0.052. This indicates that most candidate boundaries do not provide strong evidence for splitting, and some boundaries are more likely to be merged or require further observation. The segments in the curve below the removal boundary line indicate that the trend homogeneity after merging is relatively strong, and the residual inflection, trend difference, and edge state difference are insufficient to support independent partitioning.

[0097] Figure 8 The highest score was approximately 0.096, corresponding to the E-N213-N214 boundary, located in the range of approximately 106km to 107km. Although the score of this boundary was not high, it exceeded the preservation boundary line, and the difference in the edge state vector was large, indicating that the propagation parameters or path reliability had changed significantly at this point. Continuing to share evolution parameters across regions may introduce errors, so it is more suitable to preserve the boundary and proceed to the split preview.

[0098] The lowest score is approximately -0.190, corresponding to the E-N225-N226 boundary, located in the range of approximately 112km to 113km. At this point, the degree of inflection of the residual spatial gradient is close to zero, the multi-scale trend differences are small, and the edge state differences are also weak. The homogeneity of the trend after merging is close to 1, indicating that the nodes on both sides are more like the same continuous evolutionary region within the current observation window, making it suitable for removing the boundary and merging.

[0099] therefore, Figure 8 This is a graphical explanation of the twin partitioning criterion formula in the main text. Its function is not to mechanically divide nodes according to a fixed mileage length, but rather to identify the true boundaries within the influence subgraph by combining residual inflection points, trend homogeneity, and propagation differences. For positions where the curve crosses the retention line, a state mapping between the original node and candidate child nodes should be established first; for positions below the removal line, merging should be performed after time axis gap alignment and fusion weight calculation.

[0100] In a preferred embodiment, the twin partition reconstruction module establishes a mapping matrix between the original node state trajectory and the candidate child node state trajectory before splitting the twin nodes. It then uses this mapping matrix to generate initial state sequences for the candidate child nodes and reconstructs directed state association edges based on the propagation order between the candidate child nodes and their upstream and downstream twin nodes. Before merging the twin nodes, the twin partition reconstruction module performs gap alignment on the time axis of the candidate twin nodes, encodes the data integrity, residual stability, and propagation consistency at the same time point as fusion weights, and uses these fusion weights to generate a merged state sequence. After splitting or merging, it retains the node correspondence and parameter inheritance relationships before and after reconstruction, forming a twin version mapping table for subsequent incremental calibration.

[0101] The mapping matrix between the original node state trajectory and the candidate child node state trajectory is established according to the mileage coverage relationship. The rows of the matrix correspond to the historical state records of the original node, and the columns of the matrix correspond to the split candidate child nodes. When the mileage range of a certain historical state record falls completely into a candidate child node, all mapping weights are allocated to the corresponding column. When crossing the candidate boundary, the weights are allocated to the adjacent columns according to the overlapping mileage ratio. The weight allocation is also corrected by combining the local observation completeness in the corresponding time slice. The initial state sequence of the candidate child node is reassembled from the mapped historical records in chronological order. The directed state association edges between the original node and the upstream or downstream node are not directly copied. Instead, the propagation delay and amplitude attenuation are re-estimated according to the order of change of the candidate child node and the adjacent node, preserving the chronological order without forcibly preserving the failed propagation parameters.

[0102] Before merging, the timeline gap alignment is based on the common observation time. For a moment when a candidate twin node is missing but other candidate twin nodes have valid data, the interpolation result is not generated immediately. Instead, the missing data is written into the alignment record, and the fusion weight is determined based on the data completeness, residual stability, and propagation consistency of each node. Nodes with complete data, stable residuals, and consistent propagation relationships with adjacent nodes receive higher fusion weights, while nodes with continuous missing data or conflicting propagation directions receive lower fusion weights. The merged state sequence is obtained by combining the states of each node at the same moment according to the fusion weights. After combination, the directed state association edges with upstream and downstream nodes are recalculated. If a new main propagation state transition occurs after merging, the merging is canceled and the original node boundaries are restored.

[0103] The twin version mapping table uses the model version number before and after each reconstruction as an index to record the original node number, the reconstructed node number, the mileage coverage relationship, the state mapping relationship, the parameter inheritance relationship, the original directed state association edges, the reconstructed directed state association edges, and the reconstruction trigger basis. When splitting a node, it records the splitting relationship of one original node corresponding to multiple new nodes. When merging nodes, it records the fusion relationship of multiple original nodes corresponding to one new node. Nodes that did not participate in the reconstruction maintain the continuity of the version mapping. After reading the twin version mapping table, the local incremental calibration module can determine which parameters can be inherited from the historical version, which parameters need to be re-estimated, and which boundary nodes need to be subject to continuity constraints, so as to avoid the loss of correspondence between historical states and calibration results due to changes in node numbers.

[0104] Further, please refer to Figure 4The local incremental calibration module expands the calibration neighborhood upstream and downstream according to the range of the anomaly source. The expansion range is determined by the propagation delay and amplitude attenuation of the directed state-related edges. The state and parameters of twin nodes outside the calibration neighborhood are set to a frozen state. The local incremental calibration module alternately updates the state evolution parameters of twin nodes and the propagation parameters of directed state-related edges within the calibration neighborhood. After each round of updates, the parameters of the boundary nodes are adjusted according to the prediction continuity at the boundary of the calibration neighborhood, and a difference index is established between the residual tensors before and after calibration. When the difference index indicates that the calibration error is spreading to the frozen region, the parameter update of this round is canceled and the calibration neighborhood is expanded according to the propagation direction before the joint update is re-executed.

[0105] The calibration neighborhood expands along directed state-related edges starting from the region of influence of the anomaly source. Upstream expansion preserves the baseline state before the anomaly occurred, while downstream expansion covers the segment where the anomaly may continue to propagate. For each edge traversed, the corresponding propagation delay and amplitude decay are read. Edges with longer propagation delays but slower amplitude decay are allowed to continue expanding, while edges with unstable propagation delays or rapidly decaying amplitudes are used as candidate stopping boundaries. If multiple combined propagation paths exist simultaneously, the expansion contribution is calculated according to the confidence level of each path, and the node with the higher total contribution is retained. The node states, node evolution parameters, and edge propagation parameters outside the calibration neighborhood are all marked as frozen. The calibration process can only read the boundary states of the frozen region and cannot modify its internal parameters.

[0106] A local joint update can be performed using the following formula:

[0107] ;

[0108] in, The calibration neighborhood is represented by h, which represents the effective observation location within the calibration neighborhood. This represents the measured settlement value. Indicates the set of parameters to be updated The generated twin predictions, This represents the set of boundaries between the calibration neighborhood and the frozen region. This represents the reference prediction provided by the frozen area at boundary e. This represents the prediction of the boundary nodes after calibration. This represents the set of parameters before calibration. , and They represent , and The corresponding terms are non-negative coefficients with a sum of 1. The first term constrains the fitting of observations within the neighborhood, the second term constrains the continuity of the boundary, and the third term restricts unfounded parameter drift. For example, the second term increases when the prediction difference at the boundary increases. The joint update will prioritize adjusting the parameters of the boundary nodes rather than changing the parameters inside the frozen region.

[0109] Please refer to Figure 9 , Figure 9 The horizontal axis represents the alternating update rounds of the local joint calibration, and the vertical axis represents the objective function value. The solid line represents the objective value formed by the observation fitting term, the boundary continuity term, and the parameter drift constraint term after each round of alternating updates, while the dashed line represents the boundary continuity threshold. This figure corresponds to the local joint calibration objective formula and is used to present the convergence process after the alternating updates of the node state parameters and directed edge propagation parameters within the calibration neighborhood.

[0110] from Figure 9 As can be seen, the objective function value gradually decreased from approximately 0.420 in the first round to approximately 0.354 in the eighth round, with an average value of approximately 0.387, showing a stable downward trend overall. This indicates that under the condition of freezing the states and parameters outside the neighborhood, both the observation fitting error and the boundary continuity error within the calibration neighborhood are improved. This decreasing process shows that the joint calibration does not replace parameters all at once, but rather adjusts alternately between state evolution parameters and propagation parameters, gradually reducing the overall objective.

[0111] Figure 9 The boundary continuity threshold is around 1.0, and the objective function values ​​in all rounds are below this threshold, indicating that the current candidate calibration version has not triggered boundary continuity instability. In the first round, the target value before calibration was approximately 0.511, and the target value after calibration was approximately 0.420, with a difference index of approximately 0.157, indicating that the initial update has brought about a significant improvement; subsequent rounds continued to decrease, but the magnitude decreased, reflecting that the local joint calibration tends to converge.

[0112] Based on the calibration records, this round of calibration neighborhood contains 6 nodes, and the frozen region contains 4 boundary nodes. The residual increment of the first frozen layer gradually decreased from approximately 0.010 to approximately 0.004, without any continuous reverse increase. Therefore, this round of update does not need to be revoked, nor does it need to expand the boundary along the propagation direction. It can be retained as a candidate calibration version, and its stability can be further verified in subsequent continuous observation windows.

[0113] therefore, Figure 9 This provides a visual explanation of the local joint calibration objective formula in the main text. Its engineering significance lies in simultaneously constraining the fitting within the neighborhood, boundary continuity, and parameter drift, avoiding the pursuit of only a decrease in local residuals at the expense of the stability of the frozen region. When the curve decreases but the residual of the first frozen layer increases in the opposite direction, the current update should be canceled and the neighborhood expanded; when the curve decreases stably and the boundary is not disturbed, the candidate calibration version can be further converted into a stable version.

[0114] During alternating updates, the directed state-associated edge parameters are first fixed and the node state evolution parameters are updated. Then, the node state evolution parameters are fixed and the propagation delay, amplitude decay, and trend similarity are updated. After completing one round, the residual tensor and boundary prediction are regenerated. The difference index is composed of the residual changes in the affected subgraph before and after calibration, the residual changes at the boundary, and the residual changes of the first-layer nodes in the frozen region. If the residual in the affected subgraph decreases and the residual of the first-layer nodes in the frozen region does not increase, the current round of updates is accepted. If the residual in the affected subgraph decreases but the first-layer nodes in the frozen region show a continuous reverse increase, it is determined that the calibration error has propagated across the current boundary. The node parameter and edge parameter updates are canceled, and the calibration neighborhood is expanded along the propagation direction where the reverse increase occurs before recalculation.

[0115] In a preferred embodiment, the local incremental calibration module stores the state evolution parameters, directed state-related edge parameters, and residual tensors before and after each node reconstruction based on a twin version mapping table, and forms a parameter migration graph for two consecutive calibrations. The parameter migration graph uses the node before reconstruction, the node after reconstruction, and the calibration boundary node as vertices, and parameter inheritance, parameter splitting, and parameter fusion as migration edges. When new settlement data causes the same anomaly source's area of ​​action to be reconstructed, the local incremental calibration module retrieves historical calibration paths consistent with the current node boundary along the parameter migration graph, uses the parameter changes in the historical calibration paths as the initial constraints for this joint update, and compares the current residual tensor with the historical residual tensor after the update is completed, retaining only the parameter migration paths that do not cause a reverse increase in residuals outside the calibration boundary.

[0116] In the parameter migration graph, parameter inheritance edges are used to connect nodes in previous and subsequent versions where the mileage coverage remains unchanged. Parameter splitting edges are used to connect an original node with multiple split nodes. When parameter fusion is used as a migration edge, it connects multiple nodes before merging with one node after merging. Each migration edge records the corresponding parameter transformation method, applicable mileage range, observation time range, and residual change after calibration. Calibration boundary nodes are used as independent vertices to preserve the continuity constraints between them and the frozen region. After two consecutive calibrations, the new version parameters and their sources are written into the parameter migration graph, so that subsequent reconstructions can trace the source of parameters along the graph structure, rather than simply re-initializing all parameters according to the latest model version.

[0117] When the same anomaly source's range of influence is split or merged again, the local incremental calibration module retrieves historical paths based on the current node's mileage boundary, propagation direction, and twin version mapping relationship. Only paths where the historical node boundary has a clear coverage correspondence with the current boundary and where there is no directional conflict between the historical main propagation state and the current combined propagation state are retained. Changes in node parameters in the historical path are used to limit the initial value range of the current parameters, and changes in edge parameters are used to limit the candidate range of propagation delay. After completing this joint update, the current residual tensor and the control residual tensor obtained by replaying the historical path are generated respectively. If a migration path causes the residual outside the calibration boundary to increase continuously, it is removed from the candidate paths and the parameter state is restored to the state when the path was not used.

[0118] In this embodiment, for line base sections with discontinuities in the observation sequence, the data integrity identifier and the measured settlement value are entered into the node status record together. Missing positions are not directly calculated in the residual tensor for the corresponding observation items, but the valid observations before and after them are still used to determine the trend direction and propagation sequence. Data repair is only performed after the anomaly interpretation branch is selected as the branch with the highest consistency. The repair value is obtained by combining the propagation results of adjacent nodes with stable directed state associated edges according to the path confidence, and the repair source, repair time range and corresponding model version are saved at the same time. When real observations are obtained later, the real observations are used to replace the repair values ​​and the relevant residuals are recalculated. The repair values ​​are not permanently used as the real state to participate in the anomaly source confirmation.

[0119] For cases where new settlement data causes changes in the direction of directed state-related edges, the subgrade settlement propagation graph construction module first retains the original edge as a historical edge and establishes a reverse candidate edge. Within the continuous observation window, the path credibility of the original and reverse directions is calculated separately. If the reverse candidate edge continues to dominate, it is converted into a main edge and the parameter sharing boundary is updated. If both directions have stable credibility, the bidirectional combined propagation state is retained. The composite residual generation module calculates the propagation consistency residual along the two directions respectively. When the anomaly source inversion module backtracks, it selects the interpretable direction based on the order of residual occurrence to avoid state breakage between model versions caused by directly deleting historical propagation relationships due to short-term direction changes.

[0120] In the case of multiple main anomalies within the same anomaly source's influence range, the anomaly source inversion module calculates the inversion residual reduction map when each main anomaly source is replaced individually, and then calculates the inversion residual reduction map when multiple main anomalies are replaced jointly. If the residual reduction range generated by the joint replacement is equal to the union of the individual ranges, then the multiple main anomalies are kept as independent source nodes and influence subgraphs are established separately. If continuous residual reduction that cannot be explained by individual replacement occurs after the joint replacement, then the multiple main anomalies and their connecting paths are merged into a composite anomaly source region. The twin partition reconstruction module prioritizes retaining the residual turning boundary on the connecting path within the composite anomaly source region and determines the local incremental calibration neighborhood based on the joint influence range.

[0121] Specifically, after each digital twin update cycle, the system generates the current version of the line subgrade settlement propagation map, residual tensor version, anomaly source label version, twin partition version, and parameter migration map version. All versions are associated with a unified mileage coordinate and a unified observation time base. During the early warning and monitoring process, the system reads the settlement status, trend status, and anomaly source label of each node in the current digital twin model, and outputs the corresponding monitoring section range according to the anomaly source's effective range and influence subgraph. When subsequent observations arrive, they do not directly overwrite the existing version, but instead form a new version and establish a correspondence with the historical version through the twin version mapping table and parameter migration map, so that the calculation process of anomaly identification, node reconstruction, and local calibration can be repeatedly executed and verified.

[0122] Preferably, the digital twin prediction sequence is jointly generated by the basic evolution parameters of each twin node, the node's own historical state, and the propagation results of the upstream directed state association edges. The basic evolution parameters describe the state continuation of the node when there is no external propagation input, and the edge propagation parameters describe the time delay, magnitude, and direction of the upstream changes reaching the current node. When a node is split, the basic evolution parameters are inherited according to the twin version mapping table and corrected separately in the local incremental calibration. When a node is merged, multiple basic evolution parameters form a merge initial value according to the fusion weight. The prediction process retains the source identifiers of the node's own terms and the propagation input terms, and can distinguish between the node's own prediction bias and the propagation prediction bias when generating composite residuals and comparing anomaly interpretation branches.

[0123] In a preferred embodiment, after the digital twin model completes local incremental calibration, it does not immediately set all new parameters to the stable version. Instead, it retains the pre-calibration version, the candidate calibration version, and the boundary extension version. The candidate calibration version continuously generates prediction sequences and compares them with the measured settlement sequences in subsequent continuous observation windows. If the candidate calibration version maintains a low residual within the influence subgraph and does not cause the residual of the first-layer node in the frozen area to increase in the opposite direction, it is converted to the current stable version. If the boundary extension version can reduce the residual at the boundary without changing the state of the distant stable node, the boundary extension version is adopted. If neither version can maintain boundary continuity, it reverts to the pre-calibration version and re-executes the anomaly interpretation branch comparison.

[0124] Furthermore, a consistency check is set between the twin partition reconstruction and the local incremental calibration. After the twin partition reconstruction is completed, an uncalibrated prediction is generated using inherited parameters. If the residual direction generated by the uncalibrated prediction at the new boundary is consistent with the original anomaly propagation direction, then the local incremental calibration is entered. If the residual direction at the new boundary is opposite to the original anomaly propagation direction, then the residual spatial gradient inflection and edge state vector difference of the candidate boundary are rechecked. If necessary, the original boundary is restored or the split position is adjusted. After the local incremental calibration is completed, it is checked again whether the anomaly source's influence range is still completely covered by the reconstructed nodes. If the anomaly source is located outside the node boundary, the influence subgraph is regenerated and the calibration neighborhood is updated.

[0125] In this embodiment, the subgrade settlement propagation map, residual tensor, inversion residual reduction map, twin version mapping table, and parameter migration map are all stored in a traceable data association manner. Any node state record can be associated with the corresponding measured settlement data, digital twin prediction data, edge state vector, and model version. Any anomaly source label can be associated with the candidate set, local state replacement range, branch consistency comparison result, and influence subgraph. Any parameter update can be associated with the calibration neighborhood, frozen region, boundary continuity constraint, and difference index, so that the subgrade settlement status of the entire line maintains a continuous data reference relationship during the process of node boundary changes and model version changes.

Claims

1. A railway subgrade settlement early warning and monitoring system based on digital twins, characterized in that, It includes a subgrade settlement propagation map construction module, a composite residual generation module, an anomaly source inversion module, a twin partition reconstruction module, and a local incremental calibration module; The track subgrade settlement propagation map construction module maps the settlement state of each track subgrade section to twin nodes with propagation direction according to the continuous relationship of railway mileage, and establishes directed state association edges between adjacent twin nodes. The composite residual generation module generates time-series residuals, propagation consistency residuals, and multi-scale trend residuals based on measured settlement sequences and digital twin prediction sequences. The anomaly source inversion module determines the anomaly source and its influence subgraph based on the spatial gradient, duration and propagation direction of the three types of residuals. The twin partitioning reconstruction module adjusts the partitioning boundary of the twin nodes according to the aggregation pattern of the anomaly source in the influence subgraph; The local incremental calibration module updates the propagation parameters and state evolution parameters only for the adjusted influence subgraph, and writes the update results into the digital twin model.

2. The railway subgrade settlement early warning and monitoring system based on digital twin as described in claim 1, characterized in that, The line subgrade settlement propagation map construction module performs segment alignment on the historical settlement sequence, the current settlement sequence and the digital twin prediction sequence based on unified mileage coordinates, encodes the sequential relationship of settlement changes between adjacent segments as directed state association edges, and establishes an edge state vector composed of propagation time delay, amplitude attenuation and trend similarity for each directed state association edge. The subgrade settlement propagation diagram construction module also forms a parameter sharing boundary based on the stability of the edge state vector within the continuous observation window, so that twin nodes located within the same parameter sharing boundary share the basic evolution parameters, and twin nodes crossing the parameter sharing boundary retain independent evolution parameters. When new settlement data arrives, only the directed state-related edge and the corresponding edge state vector associated with the new settlement data are updated.

3. The railway subgrade settlement early warning and monitoring system based on digital twins according to claim 1, characterized in that, The composite residual generation module calculates the temporal residual between the measured settlement value and the digital twin prediction value, the propagation consistency residual between the target twin node and its upstream twin node, and the trend difference residual of the same twin node in the short-term window, medium-term window and long-term window, respectively, according to the same time base, and arranges the three types of residuals into residual tensors according to mileage position and time position. The anomaly source inversion module performs reverse backtracking on the residual tensor along the directed state association edge of the subgrade settlement propagation diagram. It constructs an anomaly source candidate set based on the directional consistency, scale consistency, and persistence consistency of the residual increment between adjacent twin nodes, and determines the anomaly source location and anomaly source range according to the interpretability coverage of the downstream residuals by the candidate locations.

4. The railway subgrade settlement early warning and monitoring system based on digital twin as described in claim 1, characterized in that, The twin partition reconstruction module extracts the turning points of the residual spatial gradient within the range of the anomaly source, reconstructs the line base segments between adjacent turning points into candidate twin nodes, and performs splitting or merging based on the trend homogeneity within the candidate twin nodes and the propagation difference between the candidate twin nodes. During the splitting process, the twin partition reconstruction module allocates the state history of the original twin node to the split twin node according to the mileage position, and retains the time order of the original state-related edges. During the merging process, the twin partition reconstruction module forms a merging state sequence based on the data integrity of each candidate twin node; The local incremental calibration module uses the reconstructed node boundary as the calibration boundary and jointly updates the state evolution parameters and directed state association edge parameters within the calibration boundary.

5. The railway subgrade settlement early warning and monitoring system based on digital twins according to claim 2, characterized in that, The line subgrade settlement propagation graph construction module establishes multiple candidate propagation paths for each directed state-associated edge, maps the state changes of the upstream twin node to the downstream twin node with different propagation time delays, and forms path credibility based on the reconstruction error of each candidate propagation path on the measured settlement changes downstream. When the path credibility of multiple candidate propagation paths is close, multiple propagation delays and their weights are retained as the combined propagation state of the directed state associated edges. When the path credibility of a single candidate propagation path continues to dominate, the corresponding propagation delay is solidified into the main propagation state. The parameter sharing boundary is adjusted based on the difference in the combined propagation state of adjacent directed state associated edges, and the position where the main propagation state transitions is set as the boundary position where cross-regional sharing of evolution parameters is prohibited.

6. The railway subgrade settlement early warning and monitoring system based on digital twins according to claim 3, characterized in that, The anomaly source inversion module performs local state replacement on each candidate position in the anomaly source candidate set, replaces the measured settlement segment corresponding to the candidate position with the digital twin prediction segment, and recalculates the propagation consistency residual and trend difference residual of the downstream twin node along the directed state association edge to obtain the inversion residual reduction map corresponding to the candidate position. The anomaly source inversion module sorts candidate locations based on the continuous mileage range of residual reduction, the degree of cross-scale preservation, and the degree of consistency with the propagation direction in the inversion residual reduction map. Candidate locations that can simultaneously reduce temporal residuals, propagation consistency residuals, and trend difference residuals are retained as main anomaly sources, while candidate locations that only reduce local temporal residuals and do not form downstream continuous responses are marked as data mismatch locations.

7. The railway subgrade settlement early warning and monitoring system based on digital twins according to claim 4, characterized in that, Before splitting the twin nodes, the twin partition reconstruction module establishes a mapping matrix between the original node state trajectory and the candidate child node state trajectory, uses the mapping matrix to generate the initial state sequence of the candidate child nodes respectively, and reconstructs the directed state association edges according to the propagation order relationship between the candidate child nodes and the upstream and downstream twin nodes. Before merging twin nodes, the twin partition reconstruction module performs gap alignment on the time axis of the candidate twin nodes, encodes the data integrity, residual stability and propagation consistency at the same time as fusion weights, and uses the fusion weights to generate a merged state sequence. After splitting or merging, the node correspondence and parameter inheritance relationship before and after reconstruction are retained to form a twin version mapping table for subsequent incremental calibration.

8. The railway subgrade settlement early warning and monitoring system based on digital twins according to claim 4, characterized in that, The local incremental calibration module expands the calibration neighborhood upstream and downstream according to the range of the abnormal source. The expansion range is determined by the propagation delay and amplitude attenuation of the directed state-associated edge. The twin node states and parameters outside the calibration neighborhood are set to a frozen state. The local incremental calibration module alternately updates the state evolution parameters of the twin nodes and the propagation parameters of the directed state-related edges within the calibration neighborhood. After each round of updates, the boundary node parameters are adjusted based on the prediction continuity at the boundary of the calibration neighborhood, and a difference index is established between the residual tensors before and after calibration. When the difference index indicates that the calibration error is spreading to the frozen region, the current parameter update is revoked and the calibration neighborhood is expanded according to the propagation direction before a joint update is performed again.

9. The railway subgrade settlement early warning and monitoring system based on digital twin as described in claim 6, characterized in that, The anomaly source inversion module generates anomaly interpretation branches for the main anomaly source and the data mismatch location, respectively. The anomaly interpretation branches include a state change branch that retains the measured settlement segment, a data repair branch that replaces the measured settlement segment with the propagation results of adjacent twin nodes, and a model drift branch that keeps the observation data unchanged and adjusts the digital twin evolution parameters. The anomaly source inversion module calculates the residual tensor corresponding to each anomaly interpretation branch, and determines the branch consistency based on the reduction range of downstream continuous residuals and the degree of preservation of upstream stable residuals by the anomaly interpretation branch. The anomaly interpretation branch with the highest branch consistency is written into the anomaly source label, while the remaining anomaly interpretation branches are reserved as candidate branches for re-comparison when new settlement data arrives.

10. The railway subgrade settlement early warning and monitoring system based on digital twins according to claim 7, characterized in that, The local incremental calibration module stores the state evolution parameters, directed state-related edge parameters, and residual tensors before and after each node reconstruction based on the twin version mapping table, and forms a parameter migration graph for two consecutive calibrations. The parameter migration graph uses the pre-reconstruction node, the post-reconstruction node, and the calibration boundary node as vertices, and parameter inheritance, parameter splitting, and parameter fusion as migration edges. When new settlement data causes the same anomaly source's influence range to be reconstructed again, the local incremental calibration module searches for historical calibration paths consistent with the current node boundary along the parameter migration graph, uses the parameter changes in the historical calibration paths as the initial constraints for this joint update, and compares the current residual tensor with the historical residual tensor after the update is completed, retaining only the parameter migration paths that do not cause the residual outside the calibration boundary to increase in the opposite direction.

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