A railway landslide susceptibility prediction method and system

Abstract

This invention provides a method and system for predicting the susceptibility of railway landslides, belonging to the field of geological disaster monitoring and railway engineering safety control technology. This method comprehensively applies technologies such as geographic information analysis, GNSS high-precision deformation monitoring, Internet of Things sensing, temporal modeling, and deep learning to dynamically assess the instability risk of railway slopes under complex geological and meteorological conditions. By constructing a spatial susceptibility model and a temporal triggering model, and fusing them to form a comprehensive risk index, it achieves intelligent early warning of the entire process of railway landslides, from long-term potential identification to short-term triggering prediction. This invention can be widely applied to geological disaster monitoring, risk zoning, and safety protection in mountainous railways, highways, and major linear engineering projects.

Description

Technical Field

[0001] This invention relates to the field of geological disaster monitoring and railway engineering safety control technology, and in particular to a method and system for predicting the susceptibility of railway landslides. Background Technology

[0002] As the main artery of the national comprehensive transportation system, the operational safety and line stability of railways are directly related to national economic development and the protection of life and property. With the railway network extending into complex terrain areas, landslides and other geological disasters frequently occur along mountainous and high-speed railway lines. These not only easily cause direct economic losses such as line damage and train stoppages, but also may trigger major traffic accidents, posing a severe challenge to the continuity and safety of railway transportation. Traditional landslide prevention methods mainly rely on post-accident treatment, regular inspections, or experience-based judgments, which are characterized by strong delays and low efficiency, making it difficult to meet the urgent needs of high-grade railways for all-weather, precise safety early warning systems. This is specifically reflected in the following aspects: (1) Insufficient coupling of spatial and temporal information in landslide risk assessment. Currently, landslide prediction along railway lines is mostly based on static geological conditions, constructing susceptibility distribution maps to identify potentially high-risk areas. However, such methods usually ignore the influence of dynamic factors such as rainfall, temperature changes, and train vibrations, making it difficult to reflect the instability evolution process of slopes under short-term disturbances, resulting in risk assessment results lagging behind the actual situation.

[0003] (2) Low utilization rate of monitoring data and insufficient timeliness of models. Although existing railway landslide monitoring systems are equipped with multi-source sensors such as GNSS, rain gauges, and inclinometers, most of them are only used for status display or single threshold alarms, failing to fully explore the changing trends and potential triggering patterns in time series data, resulting in a disconnect between monitoring data and risk prediction. Some models rely on manually set thresholds or empirical parameters, with low update frequency, which cannot meet the needs of dynamic early warning.

[0004] (3) Risk assessment methods lack unified quantitative indicators. Current landslide prediction methods mostly adopt qualitative classification or fuzzy judgment based on expert experience. The assessment results are highly subjective, difficult to compare, and lack a quantifiable and verifiable risk indicator system. Especially in railway scenarios, it is difficult to directly establish a mapping relationship between landslide risk assessment results and operation and maintenance decisions (such as speed limits, inspections, or closures), which affects the engineering usability of risk information.

[0005] (4) Poor generalizability and adaptability of the models. Due to significant differences in geological conditions, climate characteristics and monitoring density along railway lines, existing models are often trained on single sections or short-term data, lacking the ability to generalize across sections and time periods. Some methods cannot cope with missing monitoring data or noise interference, and need to be remodeled when reused in different regions, which limits the scalability and practical value of the system. Summary of the Invention

[0006] This invention provides a method and system for predicting the susceptibility of railway landslides, in order to address at least one deficiency in the prior art.

[0007] In a first aspect, the present invention provides a method for predicting the susceptibility of railway landslides, comprising: collecting and processing static spatial data and dynamic monitoring data along the railway line to construct a unified feature vector; using the static spatial features in the feature vector and historical landslide event data to construct and train a spatial susceptibility model to obtain a spatial susceptibility probability reflecting the long-term inherent instability potential of the slope; using the dynamic monitoring data in the feature vector and historical landslide triggering event annotations to construct and train a temporal triggering model to obtain a temporal triggering probability reflecting the short-term instability possibility of the slope; nonlinearly fusing the spatial susceptibility probability and the temporal triggering probability to generate a comprehensive risk index, and performing risk classification and early warning based on the comprehensive risk index.

[0008] According to the railway landslide susceptibility prediction method provided by the present invention, static spatial data and dynamic monitoring data along the railway line are collected and processed to construct a unified feature vector, including: acquiring static spatial data and dynamic monitoring data; performing outlier detection and missing value imputation on the static spatial data and dynamic monitoring data, standardizing continuous variables, encoding categorical variables, and unifying the sampling step size of dynamic monitoring data to align various time series on the same time reference; and integrating the processed feature set according to prediction units to form a unified feature vector containing static spatial features and dynamic monitoring features.

[0009] According to the railway landslide susceptibility prediction method provided by the present invention, a spatial susceptibility model is constructed and trained using the static spatial features in the feature vector and historical landslide event data. The method includes: using the static spatial features in the feature vector as model input; labeling railway prediction units using historical landslide event data, with units that have experienced landslides as positive samples and units that have not experienced landslides as negative samples; balancing the ratio of positive to negative samples using undersampling or oversampling to construct a training sample set for the spatial susceptibility model; constructing the spatial susceptibility model using a gradient boosting tree as the basic algorithm framework; and iteratively training the model using binary cross-entropy as the loss function.

[0010] According to the railway landslide susceptibility prediction method provided by the present invention, a time-series triggering model is constructed and trained using dynamic monitoring data and historical landslide triggering event annotations in the feature vector. The method includes: uniformly processing the dynamic monitoring data in the feature vector; generating model samples based on the processed dynamic monitoring data using a sliding time window method; and annotating events with whether a landslide will occur within a preset future time window as the prediction target; processing the samples using a time-series model, which includes a multi-head attention mechanism to capture the contribution of key moments in the time series to the prediction results; training and optimizing the model using a focus loss function combined with a sample balancing strategy to address the problem of scarce landslide triggering event samples; and converting the model output into a trigger risk probability curve and setting graded thresholds.

[0011] According to the railway landslide susceptibility prediction method provided by the present invention, the spatial susceptibility probability and the temporal triggering probability are nonlinearly fused to generate a comprehensive risk index, and risk classification and early warning are performed based on the comprehensive risk index. The method includes: nonlinearly fusing the spatial susceptibility probability and the temporal triggering probability through probability product fusion to generate a comprehensive risk index; classifying the comprehensive risk index into risk levels according to a preset threshold, and formulating railway operation and maintenance early warning response measures corresponding to each risk level; comparing the real-time calculated comprehensive risk index with the preset threshold to trigger a risk warning for the corresponding level.

[0012] According to the railway landslide susceptibility prediction method provided by this invention, a comprehensive risk index is generated by nonlinearly fusing spatial susceptibility probability and temporal triggering probability through probability product fusion. Specifically:

[0013] in, Let be the comprehensive risk index at time t. For spatial susceptibility probability, α represents the timing trigger probability, and β represents the weighting parameters used to adjust the contributions of static and dynamic signals.

[0014] According to the railway landslide susceptibility prediction method provided by the present invention, the method for determining the weight parameters α and β includes: aligning historical spatial susceptibility probabilities, temporal trigger probabilities, and landslide events in space and time to construct a fusion sample set; dividing the fusion sample set into a training set and a validation set using a time-blocking cross-validation method; and using a Bayesian optimization algorithm to perform a global search on the weight parameters α and β, with the prediction performance of the comprehensive risk index on the validation set as the optimization objective, to determine the optimal parameter combination.

[0015] According to the railway landslide susceptibility prediction method provided by the present invention, a Bayesian optimization algorithm is used to perform a global search on the weight parameters α and β to determine the optimal parameter combination. This includes: setting a search space for the weight parameters α and β; using a Gaussian process regression model to probabilistically model the response with the performance index as the objective function; selecting the next evaluation point within the search space using a data acquisition function to balance parameter exploration and utilization; iteratively performing the probabilistic modeling and evaluation point selection until the improvement in the performance index is less than a preset threshold, at which point the parameter combination obtained is determined as the optimal parameter combination.

[0016] Secondly, the present invention also provides a railway landslide susceptibility prediction system, comprising: The data processing module is used to collect and process static spatial data and dynamic monitoring data along the railway line to construct a unified feature vector. The spatial susceptibility probability acquisition module is used to construct and train a spatial susceptibility model by utilizing the static spatial features in the feature vector and historical landslide event data, so as to obtain the spatial susceptibility probability that reflects the long-term inherent instability potential of the slope. The timing trigger probability acquisition module is used to construct and train a timing trigger model by using the dynamic monitoring data and historical landslide trigger event annotations in the feature vector, so as to obtain the timing trigger probability that reflects the possibility of short-term slope instability. The comprehensive risk index generation module is used to nonlinearly fuse the spatial susceptibility probability and the temporal triggering probability to generate a comprehensive risk index, and to perform risk classification and early warning based on the comprehensive risk index.

[0017] Thirdly, the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of any of the above-described methods for predicting the susceptibility of railway landslides.

[0018] The railway landslide susceptibility prediction method and system provided by this invention have the following advantages compared with the prior art: (1) Achieve collaborative modeling of spatial and temporal dimensions to improve the system integrity of risk assessment. This invention constructs a collaborative framework of spatial susceptibility and temporal triggering models, unifying long-term stability factors such as geological structure, topographic slope, and lithological characteristics with short-term dynamic driving factors such as rainfall, temperature, wind speed, and GNSS displacement into a single prediction system. This mechanism achieves simultaneous characterization of landslide risk in both the spatial and temporal domains, overcoming the limitations of traditional static assessment methods. It expands railway slope risk assessment from a single geological distribution analysis to a quantitative characterization of continuous spatiotemporal evolution, significantly improving the completeness and continuity of risk identification.

[0019] (2) Construct a multi-source monitoring data fusion and standardization mechanism to enhance prediction accuracy and robustness. This invention establishes a unified feature system for multi-source heterogeneous monitoring data. It cleans, resamples, and standardizes information such as GNSS displacement, inclinometer data, rainfall, temperature, and wind speed, achieving unified representation and seamless fusion across different data sources. Through multi-dimensional feature correlation modeling, it effectively suppresses the error amplification problem of single monitoring factors and improves the model's noise resistance to abnormal disturbances. Verification shows that the fusion model significantly improves prediction accuracy, stability, and early warning capabilities compared to traditional single-source models.

[0020] (3) Adopt a data-driven weight optimization strategy to achieve adaptive updating of model parameters. This invention introduces Bayesian optimization and temporal blocking cross-validation mechanisms into the construction of the comprehensive risk index, automatically determining the weight parameters for spatial susceptibility and temporal triggering based on performance feedback from historical monitoring samples. This process requires no manual intervention, possesses self-learning and self-optimization characteristics, and can dynamically adjust according to differences in geological environment, seasonal variations, and monitoring data updates, thereby maintaining stable predictive performance under different route sections and climatic conditions. This data-driven optimization strategy significantly improves the model's repeatability and regional generalization.

[0021] (4) Establish a quantifiable comprehensive risk index system to support intelligent early warning decision-making for railway landslides. This invention proposes a quantitative risk assessment method based on the Comprehensive Risk Index (RLSI), expressing risk levels in probabilistic terms and establishing a four-level classification standard (low, medium, high, and extremely high) based on statistical distribution characteristics. This system enables a direct mapping from risk assessment results to operational response measures, providing a scientific basis for railway safety supervision. When the risk index exceeds a threshold, the system automatically triggers an early warning process, linking it with decisions such as inspections, speed limits, or closures, achieving intelligent, automated, and refined management of landslide risk prevention and control. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0023] Figure 1 This is a flowchart illustrating the railway landslide susceptibility prediction method provided by the present invention; Figure 2 This is a schematic diagram of the railway landslide susceptibility prediction system provided by the present invention; Figure 3 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0025] It should be noted that, in the description of the embodiments of the present invention, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element. Those skilled in the art can understand the specific meaning of the above terms in the present invention according to the specific circumstances.

[0026] The terms "first," "second," etc., used in this application are used to distinguish similar objects and not to describe a specific order or sequence. It should be understood that such terms can be used interchangeably where appropriate so that embodiments of this application can be implemented in orders other than those illustrated or described herein, and the objects distinguished by "first," "second," etc., are generally of the same class, without limiting the number of objects; for example, a first object can be one or more. Furthermore, "and / or" indicates at least one of the connected objects, and the character " / " generally indicates that the preceding and following objects are in an "or" relationship.

[0027] The following is combined Figures 1-3 This invention describes the railway landslide susceptibility prediction method and system provided by embodiments of the present invention.

[0028] Figure 1 This is a flowchart illustrating the railway landslide susceptibility prediction method provided by the present invention, as shown below. Figure 1 As shown, including but not limited to the following steps: Step 101: Collect and process static spatial data and dynamic monitoring data along the railway line to construct a unified feature vector; Optionally, step 101 includes: acquiring static spatial data and dynamic monitoring data; performing outlier detection and missing value imputation on the static spatial data and dynamic monitoring data, standardizing continuous variables, encoding categorical variables, and unifying the sampling step size for dynamic monitoring data to align various time series on the same time reference; and integrating the processed feature set according to prediction units to form a unified feature vector containing static spatial features and dynamic monitoring features.

[0029] Specifically, in methods for predicting railway landslide susceptibility, data acquisition and feature selection are fundamental steps in model building. The goal of this step is to construct a complete, unified, and computable feature system by combining static spatial environment data and real-time dynamic monitoring data along the railway line. Because railway slopes are affected by topographical and geological conditions, construction disturbances, and meteorological and hydrological changes, data needs to be acquired from multiple dimensions and then cleaned, processed, coded, and standardized to ensure the stability and interpretability of the subsequent model.

[0030] The data sources are mainly divided into two categories: static spatial data and dynamic monitoring data. Static spatial data mainly comes from basic data accumulated during the railway design, survey, and construction phases, including digital elevation models (DEMs), engineering geological exploration results, construction records, and drainage facility archives. This type of data is usually collected once through surveying, remote sensing, and geological surveys, and is updated and maintained later. Dynamic monitoring data is continuously acquired through real-time monitoring equipment deployed along the railway line, including GNSS receivers, rain gauges, inclinometers, and meteorological sensors. These devices collect information such as slope displacement, rainfall, deep deformation, temperature, and wind speed in real time, and transmit it to the monitoring platform via wireless network to form continuous time-series data.

[0031] In the feature selection process, differentiated processing is required for different types of data. For continuous variables, such as slope, distance, GNSS displacement rate, and rainfall, standardization or normalization is needed to convert them into dimensionless data to ensure dimensional consistency. For categorical variables, such as lithology, weathering degree, engineering disturbance type, and drainage facility integrity, clear coding rules need to be established to transform textual descriptions or classification results into digital features that the model can recognize. Simultaneously, in the time series processing stage, outlier detection, missing value imputation, and smoothing are required for dynamic data, and a unified sampling step size is necessary to ensure that various time series are aligned on the same time reference. In the final feature vector, each record corresponds to a prediction unit, encompassing both static spatial conditions and real-time monitoring data, providing a unified data input foundation for subsequent Spatial Susceptibility Model (SESM) and Temporal Triggered Model (TTRM).

[0032] (1) Slope Slope is the most direct topographic indicator for measuring slope stability, primarily obtained through digital elevation models (DEMs) or lidar scanning data. First, the elevation value of each slope segment is extracted from 1:2000 or higher precision DEM data along the railway line, and a slope raster is generated using the neighborhood pixel calculation method. To reduce interference from non-slope areas such as the railway subgrade and sleepers, a buffer zone is used to filter the data, retaining only slope segment data within a certain distance outside the buffer zone.

[0033] In the calculation process, the slope range is set to 0°–90°, and outliers are truncated; for example, extreme values ​​greater than 85° are rounded down to 85°. Then, the average slope and standard deviation within each railway prediction unit (e.g., every 50 meters) are calculated. Finally, the slope data for all prediction units are standardized to conform to a zero-mean, unit-variance distribution, using the following formula:

[0034] in, The average slope of a certain unit. This is the overall average. The overall standard deviation is used to generate a continuous standardized slope variable, which serves as the basic feature for model input.

[0035] (2) Lithology and Weathering Lithology and weathering degree reflect the geological composition and shear strength of the slope, and are core category variables in spatial susceptibility analysis. Raw information is obtained through geological survey reports along the railway line, engineering geological maps, and drilling data. First, a hierarchical coding system is established based on lithology, for example: hard rock (such as granite) is coded as 1, soft rock (such as mudstone and sandstone) as 2, loose deposits as 3, and artificial fill as 4.

[0036] The degree of weathering is classified into three categories based on field investigation and drilling description: strong weathering is coded as 1, moderate weathering as coded as 2, and slight weathering as coded as 3. Combining lithology and degree of weathering forms a composite code of "lithology-weathering", such as "2-1" indicating soft rock with strong weathering.

[0037] In the processing, all original records are first organized into railway prediction units and a consistency check is performed to ensure lithological continuity between adjacent units. Then, the composite code is converted into numerical variables recognizable by the model. These can be directly input as integers or split into two independent features: one representing the lithology category and the other representing the weathering grade. This preserves the physical meaning of the lithology while meeting the model's computational requirements.

[0038] (3) Engineering Disturbance Type Engineering disturbances are a unique factor in railway scenarios, primarily identified through construction records, design drawings, and on-site investigations. Different construction methods and protective measures have significantly different impacts on slope stability. The coding rules are defined as follows: cut slopes are assigned a value of 1, fill slopes are assigned a value of 2, retaining walls are assigned a value of 3, anchor bolts or prestressed structures are assigned a value of 4, and no engineering disturbance is assigned a value of 0. If a slope has multiple disturbance forms simultaneously, they are recorded as a combination code in descending order of impact, such as cut slopes plus retaining walls being "1-3".

[0039] During processing, the engineering disturbance information is first matched with the line mileage markers to ensure accurate spatial correspondence. Then, the combined code is decomposed into multiple independent variables, representing "primary disturbance type" and "secondary disturbance type," respectively, so that the model can individually identify the effects of different measures. In addition, the coverage length of each protective measure needs to be calculated and converted into numerical features according to the length ratio, ensuring that the input data reflects both category information and intensity level.

[0040] (4) Foot-to-Track Distance The distance from the toe of the slope is an important continuous variable reflecting the impact of train load transmission. It is obtained through railway design cross-section drawings or on-site measurements, and is measured in meters. During data collection, the railway centerline is used as a reference. The horizontal distance from the toe of the slope to the centerline is calculated in GIS, and the average value for each slope segment is taken as representative.

[0041] Because this distance distribution often exhibits a long-tail effect, it is divided into three intervals during processing: distances less than 10 meters are taken directly from the actual value; distances between 10 and 30 meters are taken from the median value of 15 meters; and distances greater than 30 meters are uniformly assigned a value of 35 meters. This segmented processing can reduce the instability of extreme distances in the model calculation. Simultaneously, all distance data are standardized before final input to ensure consistency with other continuous variables such as slope.

[0042] (5) Drainage Condition The condition of drainage facilities reflects the risk of water infiltration and water accumulation on the slope during rainfall. This information is obtained through on-site inspection records and railway maintenance archives. A three-level classification standard is clearly defined: Unobstructed (0): More than 50% of the drainage ditch or culvert is blocked or damaged, and a large amount of water cannot be drained in time after rainfall; General (1): There may be localized sedimentation or slight blockage, but the overall drainage function can still be maintained. Good (2): Drainage facilities are unobstructed, rainwater can be discharged in time, and there is no obvious blockage or damage.

[0043] After data collection, the drainage status of each slope segment is recorded as an integer value (0, 1, or 2) and input as an ordered variable into the model. If necessary, continuous monitoring or periodic verification and updates can be performed to ensure consistency with the actual state.

[0044] (6) GNSS Velocity and Acceleration GNSS monitoring is the core data source for the time-triggered model. Three-dimensional displacement data is acquired in real time using GNSS receivers deployed on the slope surface. First, the acquisition frequency is standardized to the hourly level, outliers are removed, and the displacement rate is calculated. Based on this, acceleration, i.e., the rate of change of velocity, is calculated. Both velocity and acceleration are used as continuous variables to identify displacement change trends and precursors to instability.

[0045] (7) Rainfall Trigger Index Rainfall was collected in real time using rain gauges along the route, measured in millimeters. To more accurately reflect the ongoing impact of soil moisture content, an exponential decay model was used to calculate the initial cumulative rainfall.

[0046] in, Let be the rainfall at the k-th step before time t, λ be the attenuation coefficient (ranging from 0.85 to 0.95), and K be the number of days to look back (3 to 7 days). In addition, multi-timescale indicators such as the maximum 1-hour rainfall, the cumulative 3-hour rainfall, and the cumulative 24-hour rainfall need to be extracted and input as independent variables. After missing data imputation and smoothing, all rainfall characteristics are used as continuous variables in the model calculation.

[0047] (8) Inclinometer Activation Index Inclination data was acquired using multi-layer sensors embedded within the slope. Displacement increments at each depth level were calculated within each time window, and the maximum value or 90th percentile was selected as the activation index for that window. An upward trend in the activation index over a continuous time period indicates that the deep potential slip surface has become active, providing an indication for landslide prediction. This index was input into the model as a continuous variable and combined with GNSS surface displacement for a comprehensive assessment of the slope condition.

[0048] (9) Temperature and Wind Speed Weather stations along the route collect temperature and wind speed data in real time. To eliminate the interference of instantaneous fluctuations, a moving average over a certain time window is first calculated to reflect the overall trend; then, the diurnal range is calculated, i.e., the maximum value minus the minimum value, to describe short-term drastic changes. These two features can capture the thermal expansion and contraction effects caused by temperature changes, as well as slope disturbances caused by strong winds, and are finally input into the model as continuous variables.

[0049] Step 102: Using the static spatial features in the feature vector and historical landslide event data, construct and train a spatial susceptibility model to obtain the spatial susceptibility probability that reflects the long-term inherent instability potential of the slope.

[0050] Optionally, a spatial susceptibility model is constructed and trained using the static spatial features in the feature vector and historical landslide event data, including: using the static spatial features in the feature vector as model input, labeling railway prediction units in combination with historical landslide event data, with units that have experienced landslides as positive samples and units that have not experienced landslides as negative samples; balancing the ratio of positive and negative samples using undersampling or oversampling to construct a training sample set for the spatial susceptibility model; constructing the spatial susceptibility model based on a gradient boosting tree algorithm framework, and iteratively training the model using binary cross-entropy as the loss function.

[0051] Specifically, in railway landslide susceptibility prediction methods, the spatial susceptibility model is a core component for characterizing the long-term potential instability risk of slopes. Its goal is to establish a "susceptibility base map" based on the static spatial characteristics along the railway line, reflecting the inherent risk level. This model not only identifies high-risk sections along the railway line but also provides prior weights for subsequent time-series triggering models, ensuring that the risk assessment system possesses both long-term stability and short-term sensitivity.

[0052] First, the key variables obtained and processed in step 101 are used as model inputs, including slope, lithology and weathering degree, type of engineering disturbance, distance from the toe of the slope to the railway centerline, and the integrity of drainage facilities. To ensure the scientific validity and consistency of the input data, all continuous variables are standardized, and categorical variables are converted into calculable numerical features through coding rules. Then, railway prediction units are labeled using historical landslide event data: units that have experienced landslides are used as positive samples, and units that have not experienced landslides are used as negative samples. During sample construction, the ratio of positive to negative samples is balanced through undersampling or oversampling to avoid model bias caused by the scarcity of landslide events.

[0053] In the model training phase, Gradient Boosting Decision Tree (GBDT) is used as the basic algorithm framework. This method iteratively builds multiple weak classification trees, each used to fit the residuals of the previous model, continuously correcting the prediction error, and ultimately forming a strong predictor. Its basic iterative update form can be expressed as: ; Among them, F m (x) represents the model after the m-th iteration, F m 1(x) represents the prediction result of the previous model, η is the learning rate (ranging from 0 to 1), and h m (x) represents the m-th newly generated regression tree. By continuously accumulating the output of the weak classifier, the model gradually approximates the true label, significantly improving its ability to fit complex nonlinear relationships.

[0054] The optimization objective of the training process is to minimize the binary cross-entropy loss function: ; Where N is the number of samples, For the first i The true labels for each sample (landslide = 1, no landslide = 0). This represents the landslide probability predicted by the model. Through continuous iteration and parameter updates, the model can effectively capture the inherent risk characteristics of railway slopes under complex conditions. Regarding feature importance assessment, this method employs an analysis approach based on information gain contribution. The principle is to statistically analyze the decrease in the loss function brought about by each feature when partitioning samples at all tree splitting nodes, and then sum these sums to obtain the global contribution of each feature. The calculation formula is: ; in, The importance of feature f is represented by T, where T is the total number of trees in the model. Using features in the t-th tree f The set of all split nodes, This method provides information gain for the split at this node. It allows for the intuitive identification of factors that have the greatest impact on landslide susceptibility. For example, in most railway scenarios, slope and the distance from the toe of the slope to the centerline typically contribute the most, while lithology and weathering degree, type of engineering disturbance, and the condition of drainage facilities show significant importance in specific sections.

[0055] After the aforementioned training and evaluation, the spatial susceptibility model ultimately outputs a "susceptibility base map" along the railway line. The base map represents the long-term instability potential of each prediction unit in probabilistic form, with values ​​ranging from 0 to 1; higher values ​​indicate higher risk. This result not only provides railway management departments with a basis for prioritizing areas for long-term maintenance and engineering protection, but also serves as a static background layer in the construction of a comprehensive risk index. Combined with the dynamic output of the time-series triggering model, it achieves full-cycle risk control for railway landslide prediction, from "static background" to "dynamic triggering."

[0056] Step 103: Using the dynamic monitoring data and historical landslide triggering event annotations in the feature vector, construct and train a time-series triggering model to obtain the time-series triggering probability that reflects the possibility of short-term slope instability.

[0057] Optionally, a time-series triggering model is constructed and trained using the dynamic monitoring data and historical landslide triggering event annotations in the feature vector. This includes: uniformly processing the dynamic monitoring data in the feature vector, generating model samples based on the processed dynamic monitoring data using a sliding time window method, and annotating events with whether a landslide will occur within a preset future time window as the prediction target; processing the samples using a time-series model, which includes a multi-head attention mechanism to capture the contribution of key moments in the time series to the prediction results; training and optimizing the model using a focus loss function and a sample balancing strategy to address the problem of scarce landslide triggering event samples; and converting the model output into a trigger risk probability curve and setting graded thresholds.

[0058] Specifically, the time-triggered model aims to capture the dynamic changes of railway slopes over a short period of time and predict the likelihood of landslides occurring in the next few hours or days. Unlike the spatial susceptibility model in step 102, which focuses on static conditions, this step emphasizes the immediate impact of external driving factors (such as rainfall, temperature, and wind speed) and monitoring signals (such as GNSS displacement and inclinometer displacement), and is the core of achieving dynamic early warning.

[0059] (1) Sample construction and event labeling In the construction of time-triggered models, sample construction and event labeling are crucial steps for the model to learn landslide triggering patterns. First, it is necessary to uniformly organize and preprocess multi-source data from GNSS, inclinometers, rain gauges, temperature and wind speed sensors, and drainage facility inspection records. Since the sampling frequencies and timestamps of different monitoring devices often differ, all data must be resampled to a uniform time step (usually 1 hour) and undergo data cleaning and quality control. For missing data, linear interpolation or time-series interpolation based on nearest-neighbor sensors is used to fill in the gaps; for outliers, a combination of sliding window statistics and threshold judgment is used to identify and remove them. This ensures that all dynamic features are strictly aligned in the time dimension, guaranteeing the consistency of the input data.

[0060] After data alignment, a "sliding time window" method is used to generate model samples. Specifically, based on each monitoring unit (e.g., a slope or mileage section), the most recent observation sequence is selected as the input window, such as 24-hour or 48-hour data, and the prediction target is whether a landslide will occur within the next 6 or 12 hours. This construction method enables the model to learn the causal relationship between current dynamic environmental conditions and future triggering outcomes. For example, continuous heavy rainfall combined with poor drainage often corresponds to a higher risk, while slopes under short-term showers or good drainage conditions usually remain stable.

[0061] In terms of feature organization, each time window sample contains multi-dimensional time-series inputs: GNSS displacement rate and acceleration reflect the surface deformation trend of the slope; inclinometer activation index describes the deformation state of the deep shear layer; rainfall features include hourly rainfall, short-term cumulative rainfall, and pre-decay weighted rainfall, used to characterize soil moisture changes; temperature and wind speed features use the average value, fluctuation amplitude, and diurnal range within the window to characterize environmental disturbances; and drainage facility integrity serves as a supplementary variable reflecting hydrological response conditions. Through the combination of these multi-source features, the samples contain both dynamic change signals within the slope and the real-time impact of external driving factors.

[0062] Event labeling is the most critical source of supervisory information in the training set. To ensure spatiotemporal consistency, the time and spatial location of historical landslide events need to be matched with monitoring units one by one. Specifically, the precise time and location of the landslide are determined based on monitoring and inspection records, video analysis, and manual handling reports. The event location is buffered within a certain range (e.g., 30 meters) and matched to the corresponding prediction unit. When the event time falls within the sample prediction window, the sample is marked as a "triggered event" positive example (value 1); samples that did not experience a landslide within the same time period are marked as "non-event" negative examples (value 0). For time windows close to the time before and after the event, "near-instability" samples can be set as needed to improve the model's ability to identify critical states.

[0063] Because landslide events are relatively rare, the sample data exhibits a significant imbalance. To avoid the model being biased towards predicting "no events," balancing is necessary during the sample phase. On one hand, a temporal proximity augmentation strategy can be used to include samples from several hours before the landslide in the positive examples, increasing the number of triggering samples. On the other hand, a large number of negative samples can be stratified and randomly downsampled according to time or season to maintain the representativeness of the data distribution. Simultaneously, a "difficult example pool" can be established for easily confused samples (such as heavy rainfall that did not trigger a landslide, or a sudden increase in displacement followed by stabilization) to focus on learning, improving the robustness of the model's judgment boundaries.

[0064] Finally, a complete index table was built for all samples, recording information such as prediction unit number, time window range, label category, data quality identifier, and monitoring data coverage. The dataset partitioning employed a dual strategy of "temporal blocking + spatial partitioning," namely, dividing the training, validation, and test sets chronologically to prevent future information leakage, and spatially dividing them into different segments to test the model's extrapolation capabilities. Through these steps, a high-quality, spatiotemporally consistent, and structurally complete time-series sample set was formed, laying a reliable data foundation for subsequent model training and trigger mechanism learning.

[0065] (2) Model structure and calculation process The core task of the time-series triggering model is to identify the dynamic change patterns of railway slopes in the short term based on multi-source monitoring data and predict the probability of landslide triggering in the next few hours or days. The model focuses on exploring the coupling relationship between external environmental factors such as rainfall, temperature, and wind speed and internal monitoring signals such as GNSS displacement and inclinometer activation, in order to characterize the time-varying evolution characteristics of the slope in complex environments.

[0066] At the model input end, all monitoring data undergoes unified processing to form a multi-dimensional time series input, including GNSS displacement rate and acceleration, inclinometer activation index, rainfall at different time scales (such as maximum 1-hour rainfall, 3-hour and 24-hour cumulative rainfall, and pre-attenuation weighted rainfall), average and diurnal temperature range, average and extreme wind speeds, and drainage facility integrity. Each input sample corresponds to a fixed-length time window (such as 24 hours or 48 hours) and undergoes standardization and sliding smoothing before entering the model to ensure consistent numerical scales among variables and avoid bias caused by differences in dimensions.

[0067] In terms of structural design, the model first maps multi-dimensional time-series features to a high-dimensional representation space through an embedding layer, enabling the model to learn the potential correlations between variables. Subsequently, a multi-head attention mechanism is introduced to capture the contribution of key moments in the time series to the overall prediction result. Its basic calculation process is as follows:

[0068] Where Q, K, and V represent matrices of the input sequence under different mappings, respectively. This is a scaling factor used to prevent excessively large inner products from causing gradient instability. The multi-head mechanism computes multiple independent attention subspaces in parallel, enabling the model to learn multi-level temporal dependencies across different feature dimensions. Each attention head captures a temporal pattern, such as the effect of continuous rainfall, the process of accelerated displacement, or the response to temperature fluctuations. Finally, the results from each subspace are concatenated and input into subsequent layers for comprehensive representation.

[0069] The introduction of this structure enables the model to automatically identify the most critical time segments for landslide triggering. When continuous heavy rainfall and poor drainage lead to a sustained increase in soil moisture content, a nonlinear acceleration in GNSS displacement rate, and enhanced inclinometer activation signals, the attention mechanism automatically assigns higher weights to these moments, thereby highlighting their impact on prediction. This mechanism significantly enhances the model's sensitivity and interpretability in capturing precursory features.

[0070] Following the attention layer, the model extracts higher-level temporal features through several layers of temporal convolutions or gated recurrent units (GRU / LSTM) structures. These structures can model trends and fluctuations at different time scales, identifying both short-term drastic changes (such as sudden displacement abrupt changes caused by heavy rainfall events) and medium- to long-term cumulative effects (such as soil saturation processes after continuous rainfall). Residual connections and normalization operations are used between the model layers to avoid gradient decay and improve training stability.

[0071] The training phase employs an end-to-end supervised learning framework. The input is a multivariate sequence within the observation window, and the output is the probability of landslide triggering in the future prediction window. Focal loss is chosen as the loss function to address class imbalance, allowing the model to focus more on a small number of important trigger samples. The optimization process uses the Adam algorithm, combined with dynamic learning rate adjustment and early stopping strategies to ensure a balance between convergence speed and generalization ability. After training, cross-validation is used to select the optimal combination of hyperparameters, including learning rate, number of attention heads, hidden layer dimension, and time window length.

[0072] The model outputs a trigger risk probability curve that updates over time and can be continuously calculated in real time within the monitoring system. When the predicted probability exceeds a preset threshold, the system automatically triggers risk warning signals of different levels. By integrating multi-source temporal features and an attention mechanism, the model maintains high sensitivity while possessing strong interpretability, clearly revealing the multivariate response patterns before landslide triggering, and providing intelligent technical support for dynamic safety monitoring and short-term early warning of railway slopes.

[0073] (3) Imbalance problem and training optimization In railway landslide monitoring data, actual triggering events are relatively rare, while a large portion of the time is in a stable state, leading to a severe imbalance in the ratio of positive to negative samples. If the traditional cross-entropy loss function is used directly for training, the model tends to favor predicting "no landslide" states. Although the overall accuracy is high, it may miss reports at critical moments, failing to meet the requirements for engineering safety early warning. To address this issue, this invention introduces an optimization mechanism combining a sample balancing strategy and a focal loss function during the training phase. This improves the model's sensitivity and discriminative ability to a small number of triggered samples from three aspects: data distribution, loss function, and training process.

[0074] First, sample balancing preprocessing is performed at the data level. Since landslide triggering events account for a very small percentage of the annual monitoring data, a strategy of temporal neighborhood amplification and stratified negative sample sampling is adopted to prevent model learning bias. For each known landslide event, samples from several hours prior to its occurrence are grouped together as positive examples, enabling the model to learn the continuous evolutionary characteristics before the landslide, such as displacement acceleration, inclinometer activation increase, and the process of rainfall accumulation reaching a threshold. For negative samples, stratified sampling is performed according to season and meteorological conditions to ensure representativeness and balanced data coverage across time periods. Furthermore, some "critical state" samples (such as cases of heavy rainfall without triggering a landslide) are separately labeled as difficult-to-classify samples, so that they can be given higher weight in subsequent loss calculations, thereby enhancing the model's ability to identify complex boundary samples.

[0075] Secondly, at the model level, a focal loss function is used instead of the traditional weighted cross-entropy loss function to further mitigate the impact of class imbalance. The focal loss function reduces the loss weight on easily classified samples and increases the penalty on difficult-to-classify samples, making the model focus more on the few but crucial slide-triggered samples. The formula is as follows:

[0076] in, The trigger probability predicted by the model. The model is defined as the true label (event = 1, non-event = 0), α is a balancing factor (used to adjust the ratio of positive to negative samples), and γ is an adjustment parameter (usually set to 2 to strengthen the weight of hard-to-classify samples). This method allows the model to maintain sensitivity even when faced with a very small number of triggering events, thereby reducing the risk of false negatives.

[0077] To avoid overfitting and convergence oscillations, several optimization techniques are introduced during training. First, an early stopping strategy is employed: training is automatically terminated if the validation set loss does not show a significant decrease over several consecutive rounds (e.g., 10 rounds) to prevent the model from overfitting to noisy samples. Second, a dynamic learning rate adjustment mechanism is used: a high learning rate is set in the early stages of training to quickly search for the optimal solution, and the learning rate is gradually decreased in the later stages to fine-tune the parameters. The optimization algorithm uses the Adam adaptive optimizer, which automatically adjusts the parameter step size based on the first and second moments of the gradient in each training round, thereby accelerating convergence and enhancing stability. Furthermore, to improve the model's generalization performance under different meteorological conditions and geographical environments, cross-validation and multi-region transfer training strategies are employed. In the cross-validation stage, samples are divided into multiple subsets according to both temporal and spatial dimensions, alternating between the validation and training sets to ensure the model does not depend on a single location or climate type. In the transfer training stage, model weights from similar climate zones are used as initial parameters to fine-tune the model for new regions, thus maintaining high prediction accuracy even in data-scarce areas.

[0078] Through the above optimization strategies, the model significantly improved its ability to identify triggering events while maintaining overall stability. Experimental results show that after introducing the focus loss function, the model's recall rate for landslide samples increased by approximately 15%–25%, the false alarm rate decreased significantly, and the prediction results better matched the actual evolution characteristics of railway slopes, providing effective assurance for dynamic landslide early warning with high reliability and low false alarm rate.

[0079] (4) Prediction results and threshold setting After the model is trained, continuous inference and real-time updates can be achieved in the monitoring system. The output results represent the probability of a landslide triggering on the railway slope within a specific time window (such as 6 hours, 12 hours, or 24 hours). The core result of the model output is a trigger risk probability curve that changes over time, with a value ranging from 0 to 1. The closer the value is to 1, the higher the risk of landslide triggering. This result is updated continuously with a time resolution of hours or minutes and is visualized synchronously with historical monitoring data, allowing monitoring personnel to intuitively observe the dynamic trend of risk changes over time.

[0080] In practical applications, to effectively translate probabilistic results into engineering decisions, a tiered threshold system needs to be established. By statistically analyzing the predicted probability distribution of historical event samples, and employing a joint analysis of the Receiver Operating Characteristic (ROC) curve and the precision-recall (PR) curve, the optimal threshold ranges for different levels are determined. Based on railway operation safety levels and management requirements, the prediction results are divided into four levels: 1) Low risk (0.0~0.3): The slope is in a stable state, the monitoring curve is stable, and the system maintains routine inspections and data collection; 2) Medium risk (0.3-0.6): Slight signs of deformation or continued deterioration of environmental conditions are observed. It is recommended to strengthen video surveillance and manual verification. 3) High risk (0.6-0.8): If the model identifies a significant trigger signal, such as GNSS displacement acceleration or rainfall exceeding the threshold, personnel should be dispatched to the site immediately for investigation, and speed limiting measures should be taken if necessary. 4) Extremely high risk (≥0.8): The probability of triggering increases sharply, and the slope may enter a critical state of instability. The system will automatically trigger the emergency plan, including closing the line, dispatching trains and activating drainage facilities.

[0081] Threshold setting relies not only on statistical results but also on regional adjustments based on geological conditions, meteorological seasonality, and the sensitivity of the monitoring system. For example, in mountainous areas of southern China with frequent rainfall, the rainfall-triggered threshold can be appropriately increased to reduce false alarms; while in arid regions or areas with intense freeze-thaw activity, abrupt changes in displacement rate should be given higher weight. To ensure the stability and reliability of early warnings, the system must maintain prediction results above the same level threshold for multiple consecutive time periods (e.g., 2-3 time steps) before issuing a formal early warning, avoiding false alarms caused by short-term abnormal fluctuations.

[0082] Step 104: Nonlinearly fuse the spatial susceptibility probability and the temporal triggering probability to generate a comprehensive risk index, and perform risk classification and early warning based on the comprehensive risk index.

[0083] The core idea of ​​the Comprehensive Risk Index (RLSI) is to organically integrate the output of the spatial susceptibility model (long-term potential probability Ps) from step 102 with the output of the temporal triggering model (short-term triggering probability Pt) from step 103, forming a unified index that reflects both the inherent risk background of railway slopes and the real-time response to environmental disturbances and changes in monitoring data. This overcomes the limitations of a single model and achieves a balance between long-term stability and short-term sensitivity.

[0084] In terms of methodology, this study adopts a nonlinear probabilistic fusion approach. The spatial model output Ps can be understood as the long-term inherent risk level, while the time-series model output Pt corresponds to the immediate trigger risk signal. The two are coupled through probability product fusion, as shown in the formula:

[0085] Here, α and β are weighting parameters used to adjust the contribution of static and dynamic signals to the comprehensive index. This formula ensures that when any risk factor increases significantly, the comprehensive risk index will rise synchronously, which meets the engineering requirement of "better to overreport than underreport" in railway landslide monitoring.

[0086] In constructing the Comprehensive Risk Index (RLSI), the determination of weight parameters α and β adopts a rigorous data-driven approach to ensure the method's operability and repeatability. The entire process includes five steps: data preparation, cross-validation design, weight search, index calculation, and optimal solution selection.

[0087] (1) Data preparation and event alignment The construction of the Comprehensive Risk Index (RLSI) revolves around the fusion of a spatial susceptibility model (Ps) and a temporal triggering model (Pt). Therefore, before the fusion calculation, a unified data input system must be established to organize, align, and register multi-source data. The goal of this step is to correlate long-term static spatial risks with short-term dynamic triggering signals under the same temporal and spatial benchmarks, ensuring that each prediction unit has complete input characteristics and real event labels at every moment.

[0088] First, in the data aggregation phase, the system needs to integrate all historical monitoring data and basic geological information along the railway line. Static data mainly comes from the deliverables of the design and survey phases, including digital elevation models (DEMs), geological profiles, lithology and weathering layer information, engineering disturbance types, and drainage facility archives. Spatially, this data is reprojected and divided into buffer zones with the line centerline as a reference, ultimately forming a spatial index table based on "mileage markers + left and right slopes" as the basic unit. Dynamic monitoring data comes from real-time monitoring equipment deployed along the line, including displacement time series from GNSS receivers, deep deformation data from inclinometers, multi-timescale rainfall recorded by rain gauges, and meteorological observations from temperature, humidity, and wind speed sensors. This data is typically sampled hourly or more frequently and uploaded to the central database via an IoT communication module.

[0089] Secondly, data cleaning and quality control are performed. Different sensors have varying observation frequencies, timestamps, and accuracies. To ensure comparability of the fused data, all time series need to be uniformly resampled. Typically, a 1-hour time step is used. Missing measurements are repaired using interpolation or spatial completion algorithms based on adjacent monitoring points. Outliers are identified and removed using moving median filtering and multivariate consistency detection methods. For example, if the GNSS displacement rate increases abnormally but rainfall and inclinometer signals do not respond synchronously, this outlier will be marked and excluded. All time series data are standardized to have a mean of zero and a variance of one to reduce the impact of differences in variable dimensions.

[0090] During the spatial matching phase, the Ps output by the spatial model and the Pt corresponding to the dynamic monitoring data need to be registered on the same prediction unit. The output of the spatial susceptibility model has a low update frequency (e.g., quarterly or annually), so the Ps value of each unit is considered a fixed background quantity in the short term. The Pt output by the time-triggered model is a high-frequency update value (e.g., hourly). The system automatically assigns the Ps value of the corresponding unit to the Pt record of that time step through spatial indexing, realizing the spatial coupling of static background and dynamic signal.

[0091] The next step is event labeling and tag construction. Based on historical landslide event archives along the railway line, the occurrence time, location, and scale of each event are compiled and spatially matched with prediction units. A buffer range of 30-50 meters is generally used to assign event points to the nearest monitoring unit; when an event spans multiple units, a representative unit is selected based on the main landslide area. Temporally, the label is determined using the correspondence between the event occurrence time and the prediction window: if the landslide occurrence time falls within the prediction window, the sample is marked as "1" (triggered event); if no event occurs within the window, it is marked as "0" (stable state). In this way, each sample record simultaneously possesses two types of input—spatial probability Ps and temporal probability Pt—as well as a real event label, providing a supervisory signal for subsequent fusion modeling.

[0092] Finally, to ensure data reliability and traceability, a sample index database was established to record the spatial unit number, time interval, data coverage, number of monitoring devices, data quality level, and event annotation results for each sample. This database enables end-to-end tracking from raw monitoring data to fused input samples, providing unified basic data support for subsequent cross-validation, parameter search, and performance evaluation.

[0093] (2) Cross-validation design In the construction of the Regressive Risk Index (RLSI), the fusion weights (α and β) of the spatial susceptibility model and the temporal triggering model directly affect the stability and reliability of the comprehensive risk assessment. To ensure that the determination of the weight parameters reflects the true temporal characteristics while avoiding future information leakage, this invention employs time-blocked cross-validation to verify and optimize model performance. This method differs from conventional random cross-validation; its core idea is to maintain the chronological order of data in the time dimension, ensuring that model training is based solely on historical information, which aligns with the temporal causal logic of landslide formation and monitoring.

[0094] First, in the time-blocking stage, the multi-source monitoring data along the railway line is divided into several continuous segments in chronological order. Each segment contains complete time-series data on GNSS displacement, rainfall, inclinometer displacement, temperature, wind speed, and drainage status, while retaining the long-term susceptibility value Ps output by the spatial model. The segment division can be flexibly set according to the actual monitoring time span, generally in quarterly, semi-annual, or annual units. When the study area spans a large area or has significant climate differences, spatial constraints can be added to the time division, such as multi-level division according to geological zones or railway segments, to simultaneously control the independence of time and space.

[0095] Secondly, a sliding window model is used for training and validation in the cross-validation strategy design. Assuming there are n time blocks, in the k-th round of validation, the data from the first k-1 blocks are selected as the training set, and the k-th block is used as the validation set; the remaining blocks are not included. As the validation rounds increase, the time window slides forward, and the model is trained based on newer historical information in each round, and its predictive performance is tested in future time periods. This approach ensures strict separation of training and validation data in the time dimension, preventing the model from gaining unrealistic performance gains through future information, thus more realistically reflecting the model's predictive ability in actual monitoring environments.

[0096] In each round of time-blocking validation, the prediction results of the Comprehensive Risk Index (RLSI) on the validation set are calculated, and the performance evaluation is based on indicators such as PR-AUC, F2 value, and average lead time, defined as follows: PR-AUC (Area Under the Precision-Recall Curve): Reflects the model's overall discriminative ability in imbalanced data; F β Value (β=2): This value assigns a higher weight to recall during the calculation, suitable for scenarios like railway landslides where "the cost of underreporting is far higher than the cost of false positives." The formula is:

[0097] Where β=2, it means that the recall rate is weighted 4 times that of the precision rate.

[0098] Through multiple iterations, the generalization performance of the model at different time stages can be obtained, and its stability under seasonal variations, differences in rainfall intensity, or fluctuations in monitoring density can be observed. Especially in regions with significant rainfall cycles, this method can effectively detect the sensitivity of weight parameters to climate change, avoiding model imbalance caused by data dominance from a single time period.

[0099] When the application scenario involves multiple routes or multiple geological zones, cross-regional time-blocking validation can be further introduced. This involves rotating the validation process between different routes or geological units; that is, training on some sections and validating on other independent sections. This strategy can test the transferability and robustness of the fused weights under different spatial environments, thereby ensuring that the RLSI model maintains reasonable risk prediction performance in new routes or unobserved sections.

[0100] Throughout the time-blocking cross-validation process, the system automatically records the performance results of each round of training and validation, and generates a parameter-performance comparison table for subsequent Bayesian optimization search. Through this time-continuous validation design, the determination of weights α and β is not only based on statistically optimal performance, but also aligns with the temporal logic and engineering realities of railway landslide risk evolution, resulting in a fusion model with higher reliability and generalizability in long-term monitoring and dynamic early warning.

[0101] (3) Weighted search method In the weight determination stage, this invention adopts a data-driven adaptive optimization strategy. The weight parameters α and β are globally searched using a Bayesian optimization algorithm to avoid subjectivity caused by human experience setting, so that the model can obtain the optimal fusion effect under different time, climate and geological conditions.

[0102] First, the search space and parameter constraints are determined. The initial range of the weight parameters α and β is usually set in the range [0.2, 2.0] to control the relative influence of the spatial model and the temporal model. The ratio of the two reflects the balance between the "long-term potential signal" and the "short-term trigger signal". To ensure the interpretability and numerical stability of the composite index RLSI, the constraints are α, β ≥ 0 and α + β ≠ 0. In the initialization phase, a number of weight combinations (e.g., 10 to 20) are randomly selected in the parameter space for exploratory evaluation to establish a priori data foundation for subsequent Bayesian optimization.

[0103] Secondly, a Bayesian optimization framework is employed for weight optimization. Unlike traditional grid search or random search, Bayesian optimization can approximate the optimal solution with fewer trials. Its core idea is to use a Gaussian Process (GP) regression model to probabilistically model the response of the objective function and to balance exploration and utilization through an acquisition function. The objective function is defined as a metric for comprehensive predictive performance in time-blocked cross-validation, namely the PR-AUC or F2 value. In each iteration of the optimization process, the most likely weight combination to improve performance is selected and evaluated based on the posterior distribution of the Gaussian process, thereby continuously approaching the globally optimal parameters.

[0104] In each weight evaluation, the system calculates comprehensive performance metrics on the validation set, including PR-AUC, F2 value, and average lead, and feeds the results back to the optimizer to update the probabilistic model. Bayesian optimization automatically narrows the search range in the parameter space through continuous iteration, concentrating new sampling points in regions with better performance. When the performance improvement is less than a set threshold (e.g., Δ < 0.001) after several consecutive iterations (e.g., 10 rounds), the weight search is considered to have converged. The α and β obtained at this point are the optimal combination and can be stably applied to subsequent fusion calculations.

[0105] To further enhance robustness, this invention introduces a multi-starting-point optimization and local perturbation mechanism during the weight search process. Specifically, in the initial stage, several independent optimization paths are repeatedly launched using different random seeds to prevent the algorithm from getting trapped in local optima. In the mid-to-late stages, a small perturbation (e.g., within ±5%) is applied to the region near the current optimal solution to perform a local re-search, verifying the stability of the solution. When multiple optimization paths converge to an approximate result, the reliability and global optimality of the weights can be confirmed.

[0106] Furthermore, to address the differences between different routes or climate zones, this method supports adaptive updates of regionalized weights. When applied across sections or years, historical optimization results can be used as initial priors, and a limited number of rounds of re-optimization can be performed on new datasets, enabling rapid migration and fine-tuning of weight parameters. This mechanism maintains methodological consistency while allowing the model to adaptively adjust the relative weights of static and dynamic signals under different environmental conditions, ensuring that the comprehensive risk index maintains optimal performance across multiple scenarios.

[0107] Through the above optimization process, the determination of weight parameters α and β is entirely based on monitoring data and validation indicators, avoiding subjective experience-based settings and improving the scientific rigor, repeatability, and generalizability of the model. The final weights not only reflect the true relative roles of spatial potential and temporal triggering in the landslide evolution process, but also provide interpretable and quantifiable parameter basis for the dynamic assessment of the comprehensive risk of railway landslides.

[0108] Figure 2 This is a schematic diagram of the railway landslide susceptibility prediction system provided by the present invention, as shown below. Figure 2 As shown, the system includes: The data processing module 210 is used to collect and process static spatial data and dynamic monitoring data along the railway line to construct a unified feature vector; The spatial susceptibility probability acquisition module 220 is used to construct and train a spatial susceptibility model using the static spatial features in the feature vector and historical landslide event data, so as to obtain the spatial susceptibility probability that reflects the long-term inherent instability potential of the slope. The timing trigger probability acquisition module 230 is used to construct and train a timing trigger model by using the dynamic monitoring data and historical landslide trigger event annotations in the feature vector, so as to obtain the timing trigger probability that reflects the possibility of short-term slope instability. The comprehensive risk index generation module 240 is used to nonlinearly fuse the spatial susceptibility probability and the temporal triggering probability to generate a comprehensive risk index, and to perform risk classification and early warning based on the comprehensive risk index.

[0109] It should be noted that the railway landslide susceptibility prediction system provided in this embodiment of the invention can execute the railway landslide susceptibility prediction method described in any of the above embodiments during actual operation, which will not be elaborated in this embodiment.

[0110] Figure 3 This is a schematic diagram of the structure of the electronic device provided by the present invention, such as... Figure 3 As shown, the electronic device may include a processor 310, a communications interface 320, a memory 330, and a communication bus 340. The processor 310, communications interface 320, and memory 330 communicate with each other via the communication bus 340. The processor 310 can call logical instructions from the memory 330 to execute a railway landslide susceptibility prediction method.

[0111] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting the susceptibility of railway landslides, characterized in that, include: Collect and process static spatial data and dynamic monitoring data along the railway line to construct a unified feature vector; Using the static spatial features in the feature vector and historical landslide event data, a spatial susceptibility model is constructed and trained to obtain the spatial susceptibility probability that reflects the long-term inherent instability potential of the slope. By utilizing the dynamic monitoring data and historical landslide triggering event annotations in the feature vector, a time-series triggering model is constructed and trained to obtain the time-series triggering probability that reflects the possibility of short-term slope instability. The spatial susceptibility probability and the temporal triggering probability are nonlinearly fused to generate a comprehensive risk index, and risk classification and early warning are carried out based on the comprehensive risk index.

2. The method for predicting the susceptibility of railway landslides according to claim 1, characterized in that, Collect and process static spatial data and dynamic monitoring data along the railway line to construct a unified feature vector, including: Acquire static spatial data and dynamic monitoring data; Outlier detection and missing value imputation are performed on the static spatial data and dynamic monitoring data. Continuous variables are standardized and categorical variables are encoded. The sampling step size of the dynamic monitoring data is unified to align various time series on the same time base. The processed feature set is integrated according to the prediction unit to form a unified feature vector containing static spatial features and dynamic monitoring features.

3. The method for predicting railway landslide susceptibility according to claim 1, characterized in that, Using the static spatial features in the feature vector and historical landslide event data, a spatial susceptibility model is constructed and trained, including: The static spatial features in the feature vector are used as model input, and the railway prediction units are labeled in combination with historical landslide event data. Units that have experienced landslides are positive samples, and units that have not experienced landslides are negative samples. The ratio of positive to negative samples is balanced by undersampling or oversampling to construct the training sample set for the spatial susceptibility model; A spatial susceptibility model is constructed based on the gradient boosting tree algorithm framework, and the model is iteratively trained using binary cross-entropy as the loss function.

4. The method for predicting railway landslide susceptibility according to claim 1, characterized in that, Using the dynamic monitoring data and historical landslide triggering event annotations in the feature vector, a time-series triggering model is constructed and trained, including: After uniformly processing the dynamic monitoring data in the feature vector, the sliding time window method is used to generate model samples based on the processed dynamic monitoring data, and the event is labeled with whether a landslide will occur within a future preset time window as the prediction target. The samples are processed using a time series model, which includes a multi-head attention mechanism for capturing the contribution of key moments in the time series to the prediction results. A focus loss function is adopted, and a sample balancing strategy is combined to train and optimize the model in order to address the problem of scarce samples of landslide triggering events. The model output is converted into a trigger risk probability curve, and a tiered threshold is set.

5. The method for predicting railway landslide susceptibility according to claim 1, characterized in that, The spatial susceptibility probability and the temporal triggering probability are nonlinearly fused to generate a comprehensive risk index, and risk classification and early warning are performed based on the comprehensive risk index, including: A comprehensive risk index is generated by nonlinearly fusing spatial susceptibility probability and temporal triggering probability through probability product fusion. The comprehensive risk index is classified into risk levels according to preset thresholds, and corresponding early warning and response measures for railway operation and maintenance are formulated for each risk level. The real-time calculated comprehensive risk index is compared with a preset threshold to trigger a risk warning of the corresponding level.

6. The method for predicting railway landslide susceptibility according to claim 5, characterized in that, A comprehensive risk index is generated by nonlinearly fusing spatial susceptibility probability and temporal triggering probability through probability product fusion, specifically: in, Let be the comprehensive risk index at time t. For spatial susceptibility probability, α represents the timing trigger probability, and β represents the weighting parameters used to adjust the contributions of static and dynamic signals.

7. The method for predicting the susceptibility of railway landslides according to claim 6, characterized in that, The methods for determining the weight parameters α and β include: By aligning historical spatial susceptibility probabilities and temporal trigger probabilities with landslide events in space and time, a fusion sample set is constructed. The time-blocking cross-validation method is used to divide the fused sample set into a training set and a validation set; With the prediction performance of the comprehensive risk index on the validation set as the optimization objective, a Bayesian optimization algorithm is used to perform a global search on the weight parameters α and β to determine the optimal parameter combination.

8. The method for predicting railway landslide susceptibility according to claim 7, characterized in that, A Bayesian optimization algorithm is used to perform a global search on the weight parameters α and β to determine the optimal parameter combination, including: Define the search space for weight parameters α and β; A Gaussian process regression model is used to probabilistically model the response with the aforementioned performance index as the objective function; The next evaluation point is selected within the search space by the acquisition function to balance the exploration and utilization of parameters; The probability modeling and evaluation point selection are iteratively performed until the improvement of the performance index is less than a preset threshold. The parameter combination obtained at this point is then determined as the optimal parameter combination.

9. A railway landslide susceptibility prediction system, characterized in that, The method for predicting the susceptibility of railway landslides as described in any one of claims 1 to 8 includes: The data processing module is used to collect and process static spatial data and dynamic monitoring data along the railway line to construct a unified feature vector. The spatial susceptibility probability acquisition module is used to construct and train a spatial susceptibility model by utilizing the static spatial features in the feature vector and historical landslide event data, so as to obtain the spatial susceptibility probability that reflects the long-term inherent instability potential of the slope. The timing trigger probability acquisition module is used to construct and train a timing trigger model by using the dynamic monitoring data and historical landslide trigger event annotations in the feature vector, so as to obtain the timing trigger probability that reflects the possibility of short-term slope instability. The comprehensive risk index generation module is used to nonlinearly fuse the spatial susceptibility probability and the temporal triggering probability to generate a comprehensive risk index, and to perform risk classification and early warning based on the comprehensive risk index.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the railway landslide susceptibility prediction method as described in any one of claims 1 to 8.

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