Rainfall-induced landslide probability prediction method and system

Abstract

The application discloses a rainfall-induced landslide probability prediction method and system, relates to the field of geological disaster prediction and early warning, and comprises the following steps: constructing a joint probability distribution model, and generating multiple groups of random rainfall sequences; solving a water content field and a pore water pressure field by using a Richards equation; calculating soil strength parameters by using a water content-dependent shear strength degradation model; calculating a safety factor based on a limit equilibrium principle; constructing a landslide probability prediction neural network, taking environmental features and dynamic physical quantities as inputs, training by using a joint loss function containing a data-driven loss, an infiltration physical constraint loss and a mechanical constraint loss, embedding an infiltration control equation, a strength degradation model and safety factor calculation into a forward propagation calculation graph; inputting the multiple groups of rainfall sequences into the trained model, obtaining multiple landslide probability values, and outputting a regional-scale spatial distribution risk map. The application realizes probabilistic prediction of rainfall-triggered landslide risk by coupling random rainfall generation and physical constraints.

Description

Technical Field

[0001] This application relates to the interdisciplinary field of geological disaster prediction and early warning and intelligent computing, and in particular to a method and system for predicting the probability of rainfall-induced landslides. Background Technology

[0002] Rainfall-induced landslides are among the most common and severe geological hazards globally, causing significant casualties and economic losses annually. Accurately predicting the probability of landslides under rainfall-triggered conditions is crucial for disaster prevention, mitigation, and engineering safety. Currently, methods for predicting rainfall-induced landslides mainly include empirical thresholding, data-driven machine learning, and physical-mechanical modeling. Empirical thresholding establishes empirical thresholds based on historical rainfall intensity and duration, offering simplicity and speed but failing to characterize the joint correlation of multiple parameters, thus limiting prediction accuracy. Data-driven machine learning uses deep learning to fit the nonlinear relationship between rainfall and landslides, but infiltration dynamics and intensity degradation laws are not included in the training, resulting in a "black box" problem and insufficient stability under extreme conditions. Physical-mechanical modeling predicts landslides based on unsaturated seepage theory and limit equilibrium equations, offering a clear mechanism but incurring high computational costs. Geotechnical parameters rely on laboratory test calibration, making rapid regional-scale assessment difficult.

[0003] The three types of methods mentioned above generally suffer from the following drawbacks: First, the uncertainty of rainfall input is not fully considered. Rainfall processes are inherently non-stationary processes with strong randomness, and traditional methods using deterministic inputs cannot reflect the uncertainty and diversity of future rainfall scenarios. Second, physical mechanisms are disconnected from data-driven training. Physical equations are only used as offline verification tools and do not participate in network parameter optimization, leading to model outputs that may violate basic physical laws and a lack of extrapolation ability for unseen extreme conditions. Third, there is a lack of a full-chain physical constraint coupling mechanism. Rainfall modeling, infiltration calculation, intensity degradation, and instability probability prediction are usually completed by different independent modules, lacking a cross-module feedback mechanism. Rainfall statistical errors cannot affect physical constraints, physical residuals cannot correct rainfall generation parameters in reverse, and risk prediction results cannot dynamically calibrate warning thresholds, resulting in a lack of joint optimization capabilities for the overall system. Summary of the Invention

[0004] The purpose of this application is to provide a method and system for predicting the probability of rainfall-induced landslides. This method embeds a random rainfall generation model, a Richards equation infiltration model, a strength degradation model, and a slope stability analysis model into an end-to-end differentiable computational graph, enabling cross-module error backpropagation and joint optimization. Statistical consistency bias dynamically adjusts the physical constraint weights, and online calibration of landslide observation events exceeds the probability threshold, forming a complete closed loop.

[0005] To achieve the above objectives, this application provides a method for predicting the probability of rainfall-induced landslides, comprising the following steps: S1: Obtain and preprocess multi-source historical datasets, which include historical rainfall observation data, landslide sample label data, slope environmental characteristic data, and soil parameter data; S2: Based on historical rainfall observation data, construct a joint probability distribution model of rainfall events consisting of rainfall intensity, duration, and intermittent time, and generate multiple sets of random rainfall sequences; S3: The Richards equation is used as the infiltration control equation, and the random rainfall sequence is used as the boundary condition. The water content field and pore water pressure field are solved in the differentiable computational diagram. S4: Based on the water content field, the cohesion and internal friction angle of the soil are calculated using a water content-dependent shear strength degradation model. S5: Based on the principle of limit equilibrium, the slope safety factor is calculated in the neural network calculation diagram according to the pore water pressure field, soil cohesion and internal friction angle, and the stability is judged. S6: Construct a landslide probability prediction neural network with embedded physical information. The slope environmental characteristics data, water content field, pore water pressure field, soil cohesion and internal friction angle, and slope safety factor are used as inputs, and the landslide probability is used as output. The network is trained using a joint loss function that includes data-driven loss, infiltration physical constraint loss, and mechanical constraint loss. S7: Input the multiple sets of rainfall sequences generated in step S2 into the trained landslide probability prediction neural network to obtain multiple landslide probability values, calculate the average landslide probability, maximum landslide probability and exceedance probability, and output a spatial distribution risk map at the regional scale.

[0006] Preferably, the preprocessing specifically includes: Based on the standard that the continuous rainless period exceeds a set threshold, historical rainfall observation data are divided into rainfall events; through spatial registration and temporal matching technology, landslide sample labels are mapped with corresponding slope environmental characteristics, soil parameters and rainfall event characteristics in a multidimensional way; the preprocessed multi-source historical dataset is divided into training set, validation set and test set according to the proportion.

[0007] Preferably, step S2 specifically includes: Each rainfall event is defined as a triple containing rainfall intensity, duration, and interval. A joint probability distribution model of rainfall intensity, duration, and interval time was constructed using a parametric model; By using historical rainfall observation data, the parameters of the parameterized model are optimized through maximum likelihood estimation; Construct a conditional probability model to generate rainfall sequences; Statistical consistency constraints are imposed to ensure that the generated rainfall series is consistent with historical observation data in terms of mean and variance; Multiple sets of random rainfall sequences were generated using Monte Carlo sampling to serve as future rainfall scenarios.

[0008] Preferably, the Richards equation in step S3 is a one-dimensional vertical Richards equation, expressed as: ; in, This refers to the volumetric moisture content. The unsaturated permeability coefficient, As the matrix potential, Vertical depth t For time; The surface uses flux boundary conditions, which switch to constant head boundary conditions when the rainfall intensity exceeds the saturated permeability coefficient, and the bottom uses free drainage boundary conditions. The relationship between water content and matrix potential was established using the van Genuchten model, and the unsaturated permeability coefficient was established using the Mualem model. The Richards equations were numerically solved using the finite difference method to obtain the water content field and pore water pressure field.

[0009] Preferably, the moisture content-dependent shear strength degradation model in step S4 includes: Cohesion degradation model: ; Degeneracy model of internal friction angle: ; in, The initial cohesion, The initial internal friction angle, This is the cohesion attenuation coefficient. This is the coefficient for attenuation of the internal friction angle.

[0010] Preferably, the slope safety factor in step S5 is calculated using a simplified infinite slope model: ; Where γ is the unit weight of the soil. The depth of the slip surface. The slope angle is... u Pore ​​water pressure; when When the slope is determined to be in an unstable state; The stability of the slope is determined at that time.

[0011] Preferably, the landslide probability prediction neural network in step S6 employs a multilayer perceptron network, specifically including: The input layer is used to receive spliced ​​vectors of slope environmental feature data and water content field, pore water pressure field, cohesion, internal friction angle, and slope safety factor; The hidden layers are set to 4 layers, with the number of nodes being 256, 128, 64, and 32 respectively, decreasing in a funnel shape; The output layer has one node that outputs the landslide probability. The hidden layer activation function uses the ReLU function; The output layer activation function uses the Sigmoid function; A Batch Normalization layer and a Dropout layer are inserted between each hidden layer, with the Dropout drop rate set to 0.3.

[0012] Preferably, the joint loss function in step S6 is as follows: ; in, These are the infiltration physical constraint loss weights and mechanical constraint loss weights, respectively. Data-driven loss Using binary cross-entropy loss: ; in, Landslide labels (1 indicates a landslide has occurred, 0 indicates no landslide has occurred). The number of samples; Infiltration physical constraint loss For the residuals of the Richards equation: ; in, The set of collocation points within the computational domain; Mechanical constraint loss For the consistency loss of the safety factor: ; For samples of landslides that have already occurred ( =1) Punishment >1, for samples where no landslides occurred ( =0) Punishment <1.

[0013] Preferably, the average landslide probability, maximum landslide probability, and exceedance probability are expressed as follows: ; ; ; in, For indicator functions, To preset risk thresholds, For the first i The probability of landslides corresponding to a set of rainfall sequences. N This represents the number of random rainfall sequence groups.

[0014] A rainfall-induced landslide probability prediction system employs a rainfall-induced landslide probability prediction method, comprising: The data acquisition module is used to acquire and preprocess historical datasets from multiple sources. The rainfall scenario generation module is used to construct a joint probability distribution model of rainfall events based on historical rainfall observation data, consisting of rainfall intensity, duration, and intermittent time, and generate multiple sets of random rainfall sequences; The infiltration calculation module is used to solve the water content field and pore water pressure field in a differentiable computational graph by using the Richards equation as the infiltration control equation and random rainfall sequence as the boundary condition. The strength degradation calculation module is used to calculate the cohesion and internal friction angle of soil based on the water content field and using a water content-dependent shear strength degradation model. The safety factor calculation module is used to calculate the slope safety factor and determine stability based on the limit equilibrium principle, according to the pore water pressure field, soil cohesion and internal friction angle in the neural network calculation diagram. The physical constraint training module is used to construct a landslide probability prediction neural network with embedded physical information. It takes slope environmental feature data, water content field, pore water pressure field, soil cohesion and internal friction angle, and slope safety factor as inputs and landslide probability as output. It is trained using a joint loss function that includes data-driven loss, infiltration physical constraint loss and mechanical constraint loss. The risk output module is used to input multiple sets of rainfall sequences into a trained landslide probability prediction neural network to obtain multiple landslide probability values, calculate the average landslide probability, maximum landslide probability and exceedance probability, and output a spatial distribution risk map at the regional scale.

[0015] Therefore, the above-mentioned method and system for predicting the probability of rainfall-induced landslides has the following advantages and beneficial effects: (1) This application constructs a joint probability distribution model of the triplet of rainfall intensity-duration duration-intermittent duration and performs Monte Carlo sampling, which can generate multiple sets of possible future rainfall sequences. This overcomes the limitations of traditional methods that rely on a single historical or designed rainstorm input, and thus can quantify the probability of landslides under different rainfall scenarios (such as mean, maximum and exceedance probability) in a statistical sense.

[0016] (2) This application introduces the consistency of the unsaturated seepage equation residuals and safety factor into the joint loss function of the neural network, thereby subjecting the model training process to the constraints of hydrological and geotechnical laws. This physical constraint mechanism can reduce the network output of prediction results that violate physical common sense and improve the prediction stability of the model under extreme working conditions.

[0017] (3) Automatic inversion of regional physical parameters, reducing manual calibration: In traditional physical models, soil mechanical parameters (such as cohesion attenuation coefficient) are automatically retrieved. Friction angle attenuation coefficient These parameters previously required cumbersome indoor experiments. This application sets these parameters as learnable variables in the end-to-end computational graph, and achieves parameter inversion through joint training with landslide historical data and physical constraints, reducing the dependence on detailed geological survey data and making parameter estimation more suitable for regional scales.

[0018] (4) Balancing accuracy and efficiency, suitable for regional risk early warning: The method in this application maintains good prediction results while having high regional assessment efficiency. By using the trained model to simulate multiple rainfall scenarios, the landslide risk assessment output for an area of ​​over 100 square kilometers can be completed in just a few seconds, which can support large-scale rapid early warning.

[0019] (5) Forming a cross-module dynamic feedback closed loop to improve the overall collaborative optimization capability of the system: This application drives the adaptive adjustment of physical constraint weights through statistical consistency deviation, so that rainfall generation and infiltration, intensity degradation and slope stability analysis form a feedback loop; subsequent landslide prediction errors can be reversed to correct the preceding physical parameters and network weights, avoiding the error accumulation caused by traditional independent modules; forming a dynamic coupling closed loop between multiple modules to realize the joint optimization of data-driven feature learning and physical law constraints.

[0020] (6) Achieve online evolution of risk threshold to improve long-term operational stability and regional generalization ability: This application uses newly added landslide observation events to calibrate the exceedance probability threshold in real time; automatically adjusts the threshold to balance the false alarm rate and the false alarm rate to achieve optimal prediction reliability; enables the risk discrimination boundary to evolve dynamically with time, regional geological conditions and climate change; improves the model's generalization ability in unobserved areas and under extreme rainfall conditions, and ensures long-term operational stability and the accuracy of regional landslide risk prediction.

[0021] The technical solution of this application will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of a rainfall-induced landslide probability prediction method according to this application; Figure 2The diagram below illustrates the principle of joint distribution modeling and multi-scenario generation of rainfall triplet in this application embodiment; where (a) is the generated rainfall time series (scenario 1, total rainfall = 911 mm) diagram, (b) is the IDG joint distribution diagram, (c) is the edge distribution diagram of intensity|, and (d) is the statistical consistency verification diagram; Figure 3 The diagrams shown are schematic diagrams of infiltration calculation and water content field response using the Richards equation in the embodiments of this application; where (a) is a vertical profile of water content under light rain (2 mm / h, 24h), (b) is a vertical profile of water content under moderate rain (5 mm / h, 12h), (c) is a vertical profile of water content under heavy rain (15 mm / h, 6h), (d) is a spatiotemporal response diagram of water content under light rain (2 mm / h, 24h), (e) is a spatiotemporal response diagram of water content under moderate rain (5 mm / h, 12h), and (f) is a spatiotemporal response diagram of water content under heavy rain (15 mm / h, 6h). Figure 4 This is a schematic diagram illustrating the relationship between moisture content and strength degradation parameters in the embodiments of this application; where (a) is the cohesion degradation model. Figure (b) shows the degradation model of the internal friction angle. Figure (c) shows the overall strength degradation model (normal stress). =50.0kPa) Figure, (d) is the percentage of relative intensity degradation; Figure 5 This is a schematic diagram of the model architecture and joint loss function in the embodiments of this application; Figure 6 The following are the statistical outputs and spatial distribution maps of landslide risks under multiple scenarios in this application embodiment; where (a) is a sample point uncertainty analysis map, (b) is a probability mean map, (c) is a probability maximum map, (d) is a standard deviation (dispersion) map, (e) is an exceedance probability (>0.5) map, and (f) is a risk level zoning map; Figure 7 This is a diagram illustrating the disaster-causing mechanism and physical constraint coupling framework of rainfall-induced landslides in the embodiments of this application. Detailed Implementation

[0023] The following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0024] Unless otherwise defined, the technical or scientific terms used in this application shall have the ordinary meaning as understood by a person of ordinary skill in the art to which this application pertains.

[0025] The terms "comprising" or "including," as used in this application, mean that the element preceding the term encompasses the element listed after the term, and do not exclude the possibility of encompassing other elements as well. The terms "inner," "outer," "upper," and "lower," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this application. When the absolute position of the described object changes, the relative positional relationship may also change accordingly. In this application, unless otherwise expressly specified and limited, the term "attached," etc., should be interpreted broadly. For example, it can refer to a fixed connection, a detachable connection, or an integral part; it can refer to a direct connection or an indirect connection through an intermediate medium; it can refer to the internal communication of two elements or the interaction relationship between two elements. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.

[0026] Example 1: A method for predicting the probability of rainfall-induced landslides, such as Figures 1-7 As shown, it includes the following steps: S1: Obtain and preprocess multi-source historical datasets, which include historical rainfall observation data, landslide sample label data, slope environmental characteristic data, and soil parameter data; Specifically, multi-source historical datasets are acquired, including: historical rainfall observation data containing time-series information such as rainfall intensity and start and end times; landslide sample label data covering landslide location, time, and non-landslide negative samples; slope environmental feature data including slope, aspect, elevation, lithology, soil thickness, and vegetation cover index (NDVI); and soil parameter data including soil unit weight, initial moisture content, and saturated permeability coefficient. Subsequently, the raw data is preprocessed: for rainfall data, rainfall events are segmented based on a continuous rainless period exceeding a set threshold (e.g., 6 hours); through spatial registration and temporal matching techniques, landslide samples are multidimensionally associated and mapped with corresponding slope environmental features, soil parameters, and rainfall event features. Finally, the preprocessed full sample set is randomly divided into training, validation, and test sets in a 7:1.5:1.5 ratio for subsequent model construction, training, and performance evaluation.

[0027] In practical application, a mountainous area prone to heavy rainfall, covering approximately 100 square kilometers, was selected as the study area, with a DEM resolution of 30m. Hourly rainfall observation data and a database of landslide points from 2010 to 2020 were collected for this region. Environmental characteristics included slope, aspect, elevation, lithology, and vegetation cover index. Historical rainfall data were segmented into rainfall events by hour, with a "continuous rainfall event" segmentation criterion defined as a dry period exceeding 6 hours. Over 1000 rainfall event samples were extracted.

[0028] S2: Based on historical rainfall observation data, construct a joint probability distribution model of rainfall events consisting of rainfall intensity, duration, and intermittent time, and generate multiple sets of random rainfall sequences; To address the problem that traditional methods cannot characterize the uncertainty of future rainfall, this step aims to establish a parameterized joint probability distribution model of rainfall events and generate multiple sets of rainfall time series that satisfy statistical consistency constraints.

[0029] like Figure 2 As shown, step S2 specifically includes: Each rainfall event is defined as a triple containing rainfall intensity, duration, and interval. ; in: Rainfall intensity (mm / h) Duration (h) The interval time is in hours (h).

[0030] Construct the joint probability density function for the rainfall events: ; A joint probability distribution model of rainfall intensity, duration, and intermittent time is constructed using a learnable parameterized model; ; in, The set of learnable parameters for the model. The parameterized distribution function is used. The joint probability distribution model employs the Copula joint distribution model, which decomposes the joint distribution of rainfall intensity, duration, and interval into marginal distributions and related structures. In other implementations, other probabilistic models capable of characterizing the joint distribution relationships of multiple variables may also be used as the joint probability distribution model.

[0031] Using historical rainfall observation data The parameters of the parameterized model are optimized using maximum likelihood estimation: ; Considering the temporal correlation between adjacent rainfall events, a conditional probability model is constructed to generate rainfall sequences: ; in The order of temporal dependence is determined by the model based on the conditional probability distribution. Generate the rainfall at the current moment.

[0032] Imposing statistical consistency constraints ensures that the generated rainfall series remains consistent with historical observation data in terms of mean and variance: ; right and Similarly, mean and variance consistency constraints are applied. During training, these constraints are added as regularization terms to the loss function: ; Multiple sets of random rainfall sequences were generated using Monte Carlo sampling to serve as future rainfall scenarios.

[0033] ; Each sequence This represents a possible future rainfall scenario, which is used for subsequent multi-scenario landslide risk analysis.

[0034] During the model training phase, historical real rainfall sequences are used; during the risk prediction phase, generated random rainfall sequences are used.

[0035] After generating multiple sets of random rainfall sequences, a statistical consistency feedback mechanism is constructed: based on the deviation in mean, variance, and distribution between the generated rainfall sequences and historical observed rainfall, the weights of physical constraints in the joint loss function are adaptively adjusted. When the deviation increases, the weights of the Richards equation residual loss and the safety factor consistency loss are increased; when the deviation decreases, the weights of physical constraints are decreased.

[0036] In practical applications, for each rainfall event, a triplet is calculated. Rainfall intensity The cumulative rainfall of the event divided by its duration. This represents the number of consecutive hours of rainfall. This represents the time interval between the end of the previous rainfall event and the start of this event. A joint probability model of triples is constructed using all samples. In this embodiment, a Copula function combined with the marginal Gamma distribution is used to fit the distribution. During training, model parameters are obtained through maximum likelihood estimation, and a mean consistency regularization term is introduced to ensure that the mean and variance of the generated data are consistent with historical data. Then, using the trained model, Monte Carlo sampling is employed to generate 50 sets of future rainfall sequences. Each set of sequences covers the rainfall process over the next three months, with hourly resolution, corresponding to 50 possible future weather scenarios.

[0037] S3: The Richards equation is used as the infiltration control equation, and the random rainfall sequence is used as the boundary condition. The water content field and pore water pressure field are solved in the differentiable computational diagram. like Figure 3 As shown, the spatiotemporal response of water content within the slope is calculated using an unsaturated infiltration dynamics model, establishing a physical causal chain of "rainfall-moisture". In the end-to-end training phase of the model, the rainfall boundary condition input for this step is a historical real rainfall observation sequence; while in the multi-scenario risk prediction phase, the input is a Monte Carlo random rainfall sequence.

[0038] The Richards equation is a one-dimensional vertical Richards equation, expressed as: ; in, This refers to the volumetric moisture content. The unsaturated permeability coefficient, As the matrix potential, Vertical depth t For time; surface Using flux boundary conditions: ; in, for The rainfall intensity at any given time. When the rainfall intensity exceeds the saturated permeability coefficient ( When switching to constant head boundary conditions, The bottom boundary condition adopts a free drainage boundary: ,in This refers to the thickness of the soil layer.

[0039] The relationship between water content and matrix potential was established using the van Genuchten model: ; in, Residual moisture content saturated moisture content ; The unsaturated permeability coefficient is obtained using the Mualem model: ; in, For effective saturation, This is the pore connectivity parameter (usually taken as 0.5).

[0040] The Richards equations were numerically solved using the finite difference method to obtain the water rate field. and pore water pressure field : ; in, Residual moisture content saturated moisture content The density of water (1000 kg / m³) 3 ), The acceleration due to gravity (9.8 m / s²) 2 ).

[0041] The solution process is embedded in the forward propagation computation graph of the neural network, which allows the calculation process of the water content field and pore water pressure field to track the gradient, and enables the residual terms constructed based on the Richards equation to participate in the backpropagation optimization of the joint loss function.

[0042] In practical applications, each rainfall sequence is input as a surface boundary condition into a one-dimensional unsaturated seepage model. The model is solved numerically using the Richards equations, and soil weight is considered. The soil-water characteristic curves were modeled using the van Genuchten model (parameters selected based on the soil properties of the region), and the unsaturated permeability coefficients were modeled using the Mualem model. At each time step, vertical seepage simulations were performed on each grid cell to obtain the water content at different depths of the slope at the corresponding time. and pore water pressure distributed.

[0043] S4: Based on the water content field, the cohesion and internal friction angle of the soil are calculated using a water content-dependent shear strength degradation model. like Figure 4 As shown, based on the water content obtained from infiltration calculation, a degradation model of soil shear strength with water content is established, revealing the mechanical causal relationship of "water → strength".

[0044] Extending the classic Mohr-Coulomb strength criterion to a moisture-dependent form: ; in, The cohesion (kPa) is related to the moisture content. The internal friction angle is related to the moisture content. Effective normal stress (kPa) The moisture content-dependent shear strength degradation model includes: Cohesion degradation model (exponential decay): ; Internal friction angle degradation model (linear decay): ; in, Initial cohesion (kPa), Let the initial internal friction angle be (°). This is the cohesion attenuation coefficient (a learnable parameter). This is the internal friction angle attenuation coefficient (a learnable parameter).

[0045] Rainfall infiltration leads to water content As the moisture content increases, the matrix suction decreases, the interparticle cementation weakens, and the cohesion decays exponentially. The increased moisture content leads to enhanced interparticle lubrication, weakened interlocking, and a linear decrease in the internal friction angle. Both of these factors contribute to the systematic degradation of the soil's shear strength.

[0046] Based on the moisture content distribution obtained in step S3, a strength degradation model is applied to each grid cell. Let the dry-state cohesion be... Dry friction angle Degradation coefficient (Can be adjusted during training as a learning variable). From the formula... Calculate the time-varying cohesion and friction angle at each depth. This allows us to obtain the strength parameters of the slope at various points under different rainfall scenarios and times.

[0047] S5: Based on the principle of limit equilibrium, the slope safety factor is calculated in the neural network calculation diagram according to the pore water pressure field, soil cohesion and internal friction angle, and the stability is judged. Definition of safety factor: The safety factor along the potential sliding surface is defined as the ratio of the anti-slip moment to the sliding moment: ; in, For safety reasons, The total normal stress (kPa) The pore water pressure (kPa, from step S3) The shear stress is driven by gravity (kPa).

[0048] For rapid assessment at the regional scale, a simplified model with infinite slopes is adopted: ; in, The unit weight of soil (kN / m³) 3 ), The depth of the slip surface (m) The slope angle is (°).

[0049] when When the slope is determined to be in an unstable state; Slope stability is determined at that time. Considering the engineering safety margin, the early warning threshold can be set to a preset value between 1.1 and 1.3. In the construction of the joint loss function, based on... As a boundary for physical instability.

[0050] In practical applications, limit equilibrium analysis is performed on each potential sliding surface (which can be the inclined surface of each grid). An infinite slope model is used to simplify the calculation, and the normal stress is... Driving shear stress Among them, the slope direction and slope depth Determined by terrain. Calculate the safety factor. ,when The unit is considered to be at risk of landslide. Through the above calculations, the safety factor distribution for each unit in the entire region under each rainfall scenario can be obtained.

[0051] S6: Construct a landslide probability prediction neural network embedded with physical information. Inputs include slope environmental characteristics, water content field, pore water pressure field, soil cohesion and internal friction angle, and slope safety factor. The output is the landslide probability. Training is performed using a joint loss function that includes data-driven loss, infiltration physical constraint loss, and mechanical constraint loss. A differentiable computational graph is used to participate in the construction and backpropagation optimization of the joint loss function. Physical equation constraints are embedded in the neural network training to achieve a deep integration of data-driven and physical mechanisms. Richards equations, strength degradation models, and safety factor calculations are embedded in the forward propagation computational graph. Gradients can be used to correct preceding physical parameters and network weights through backpropagation, achieving end-to-end joint optimization. Strength degradation parameters are learned variables and updated synchronously with the neural network weights.

[0052] Construct a landslide probability prediction neural network embedding physical information, where the landslide probability is expressed as: ; in, This represents the probability of a landslide occurring. It is a topographic environmental feature vector (topographic slope, aspect, elevation, lithology, vegetation cover (NDVI)). For all learnable parameters (including network weights) and physical degradation parameters ).

[0053] A multilayer perceptron (MLP) network is used, where the input layer receives environmental features. With dynamic physical quantities The concatenated vector; 4 hidden layers: the number of nodes are 256, 128, 64, and 32 respectively (decreasing in a funnel shape); output layer: 1 node, outputting the landslide probability. .

[0054] Activation function: The hidden layer uses the ReLU activation function. The output layer uses the Sigmoid function: .

[0055] Regularization techniques: Batch Normalization layers are inserted between hidden layers to accelerate convergence. Dropout layers (dropout rate 0.3) are introduced to prevent overfitting.

[0056] Unlike existing technologies where modules operate independently and are transmitted serially, this application directly embeds the mathematical expressions for infiltration control equations, strength degradation models, and safety factor calculations into the forward propagation computation graph of a neural network, forming a unified end-to-end differentiable computation graph.

[0057] Specifically, this is reflected in the following three aspects: Physical equations embedded in computational graphs: Richards equations, strength degradation formulas, and safety factor calculations are not run separately in offline numerical solutions, but are embedded in computational graphs as part of the neural network forward propagation; Gradient backpropagation runs through the entire chain: During the backpropagation process, the gradient of the loss function is passed from the prediction error to the physical equation through the chain rule, realizing a closed-loop feedback of "prediction → physical correction → parameter update". Joint inversion of physical parameters: intensity degradation parameters , As a learnable variable in the computation graph, it is updated synchronously with the neural network weights during the same optimization process.

[0058] The joint loss function is as follows: ; in, These are the infiltration physical constraint loss weights and mechanical constraint loss weights, respectively. The infiltration physical constraint loss weights and mechanical constraint loss weights are adaptive weights, dynamically updated based on statistical bias. When the statistical bias increases, the infiltration physical constraint loss weights and mechanical constraint loss weights are increased; when the bias decreases, the weights are decreased.

[0059] Data-driven loss Using binary cross-entropy loss: ; in, Landslide labels (1 indicates a landslide has occurred, 0 indicates no landslide has occurred). The number of samples; Infiltration physical constraint loss For the residuals of the Richards equation: ; in, The set of collocation points within the computational domain; Mechanical constraint loss For the consistency loss of the safety factor: ; For samples of landslides that have already occurred ( =1) Punishment >1, for samples where no landslides occurred ( =0) Punishment <1.

[0060] The Richards equation, intensity degradation model, and safety factor calculation are embedded in the forward propagation computation graph of the neural network. The physical equations participate in the gradient backpropagation process during network training, rather than being used only for posterior validation. During backpropagation, the loss function gradient can flow through both the physical equations and the network layers simultaneously, achieving coordinated updates of physical parameters and network weights. Intensity degradation parameters... , As a learnable parameter, it is related to the neural network weights. Automatic optimization during end-to-end training: ; The Adam optimizer is used for training, with a recommended learning rate of 0.001 and 100-300 epochs.

[0061] By jointly inverting regional equivalent geotechnical parameters using historical landslide label data and physical constraints, it is beneficial to reduce the reliance on indoor geotechnical tests.

[0062] In practical applications, such as Figure 5 As shown, a multilayer perceptron network is constructed, with inputs including environmental features (slope, aspect, elevation, lithology, vegetation) and dynamic physical quantities (unit water content, pore pressure, strength parameters, and safety factor) output from steps S3–S5, and outputting the probability of landslide occurrence. The network structure is a funnel-shaped MLP with four hidden layers, progressively increasing in number from 256 to 128 to 64 to 32 neurons. Each hidden layer uses ReLU activation and incorporates batch normalization and dropout (dropout rate 0.3). The output layer uses Sigmoid activation mapped to (0,1). Historical landslide data is divided into training, validation, and test sets in a 7:1.5:1.5 ratio. During training, the joint loss function, Richards equation, is embedded in the forward propagation computation graph of the neural network. The difference between the water content field and Richards equation is calculated in real-time during training. The residual gradient corrects the network weights and physical parameters through backpropagation. A safety factor consistency loss penalizes samples where landslides have occurred. No landslide sample penalty occurred. Degradation parameters Together with the network weights, these parameters are learned and automatically adjusted through backpropagation. The final trained model achieved good prediction results under the test conditions of this embodiment, and the relevant results are shown in Table 1.

[0063] Table 1 Comparison of Model Results

[0064] S7: Input the multiple sets of rainfall sequences generated in step S2 into the trained landslide probability prediction neural network to obtain multiple landslide probability values. Calculate the average landslide probability, maximum landslide probability, and exceedance probability, and output a spatial distribution risk map at the regional scale, such as... Figure 6 As shown.

[0065] Multi-scenario probability calculation: For the Group of random rainfall sequences : Input step S3 to calculate the water content field and the pressure field ; Input step S4 to calculate strength parameters and ; Input step S5 to calculate the safety factor ; Input the trained landslide probability prediction neural network, and output the landslide probability. .repeat Next, we obtain the probability set: .

[0066] Output the following statistical indicators: Average landslide probability, maximum landslide probability, and exceedance probability: ; ; ; in, For indicator functions, To preset risk thresholds, For the first i The probability of landslides corresponding to a set of rainfall sequences. N This represents the number of random rainfall sequence groups. The average landslide probability reflects the average risk level under various rainfall scenarios. The maximum landslide probability reflects the extreme risk under the most unfavorable rainfall scenario, and the exceedance probability represents the proportion of scenarios where the landslide probability exceeds a threshold.

[0067] When applied at a regional scale, the above calculations are performed for each grid cell separately, outputting a spatially distributed risk map: Figure: Spatial distribution of average landslide probability; Figure: Spatial distribution of maximum landslide probability; Figure: Transcendental probability space distribution; It can be used for landslide risk zoning and early warning decision-making.

[0068] During the risk prediction phase, newly added landslide observation events are used to calibrate the exceedance probability threshold online: the false alarm rate and the missed alarm rate are statistically analyzed. When the missed alarm rate is higher than the preset value, the threshold is lowered, and when the false alarm rate is higher than the preset value, the threshold is raised, forming a closed loop of "risk prediction - disaster verification - threshold calibration".

[0069] In practical applications, 50 sets of random rainfall sequences are input into a trained landslide probability prediction neural network to obtain 50 regional landslide probability distributions. Statistical analysis of these probabilities generates various risk maps, including an average landslide probability map, a maximum landslide probability map, and a probability map showing the probability of exceeding a preset probability threshold (e.g., 0.7). These statistical indicators and spatial distribution maps can be used for landslide risk zoning and early warning decisions, providing management departments with confidence interval information on landslide probabilities.

[0070] Example 2: A rainfall-induced landslide probability prediction system employs a rainfall-induced landslide probability prediction method, comprising: The data acquisition module is used to acquire and preprocess historical datasets from multiple sources. The rainfall scenario generation module is used to construct a joint probability distribution model of rainfall events based on historical rainfall observation data, consisting of rainfall intensity, duration, and intermittent time, and generate multiple sets of random rainfall sequences; The infiltration calculation module is used to solve the water content field and pore water pressure field in a differentiable computational graph by using the Richards equation as the infiltration control equation and random rainfall sequence as the boundary condition. The strength degradation calculation module is used to calculate the cohesion and internal friction angle of soil based on the water content field and using a water content-dependent shear strength degradation model. The safety factor calculation module is used to calculate the slope safety factor and determine stability based on the limit equilibrium principle, according to the pore water pressure field, soil cohesion and internal friction angle in the neural network calculation diagram. The physical constraint training module is used to construct a landslide probability prediction neural network with embedded physical information. It takes slope environmental feature data, water content field, pore water pressure field, soil cohesion and internal friction angle, and slope safety factor as inputs and landslide probability as output. It is trained using a joint loss function that includes data-driven loss, infiltration physical constraint loss and mechanical constraint loss. The risk output module is used to input multiple sets of rainfall sequences into a trained landslide probability prediction neural network to obtain multiple landslide probability values, calculate the average landslide probability, maximum landslide probability and exceedance probability, and output a spatial distribution risk map at the regional scale.

[0071] The rainfall scenario generation module, infiltration calculation module, intensity degradation calculation module, and slope safety factor calculation module are all uniformly constructed on an end-to-end differentiable computational graph, enabling subsequent landslide prediction errors to be backpropagated and updating the physical parameters and network weights of preceding modules; specifically including: The statistical bias of the rainfall scenario generation module is adjusted by gradient information to adjust the residual weight of the infiltration equation; The moisture field output by the infiltration calculation module affects the updating of intensity degradation parameters; The cohesion and friction angle output by the strength degradation model are optimized and adjusted according to the error gradient; The calculation results of the slope safety factor calculation module are used in the backpropagation of the gradient of the loss function, so that the network weights and physical parameters converge together, thereby realizing the collaborative optimization of each module.

[0072] Therefore, this application adopts the above-mentioned rainfall-induced landslide probability prediction method and system, overcoming the limitations of traditional methods that rely on a single deterministic rainfall input, and realizing multi-scenario probabilistic prediction considering rainfall stochasticity. It improves the physical consistency and interpretability of the landslide prediction model by using the infiltration equation and shear strength criterion as constraints, reducing non-physical prediction results. It reduces the dependence of the physical model on laboratory calibration by setting soil strength degradation parameters as learnable variables and inverting equivalent parameters of the region using historical landslide data. An end-to-end physical constraint coupling framework is constructed, embedding physical equations into the neural network computation graph to achieve joint optimization, enabling rainfall stochasticity modeling, physical process inference, and probabilistic prediction to be updated collaboratively in the same training loop.

[0073] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application and not to limit them. Although this application has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of this application, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of this application.

Claims

1. A method for predicting the probability of rainfall-induced landslides, characterized in that, Includes the following steps: S1: Obtain and preprocess multi-source historical datasets, which include historical rainfall observation data, landslide sample label data, slope environmental characteristic data, and soil parameter data; S2: Based on historical rainfall observation data, a joint probability distribution model of rainfall events consisting of rainfall intensity, duration, and intermittent time is constructed, and multiple sets of random rainfall sequences are generated through Monte Carlo sampling; S3: The Richards equation is used as the infiltration control equation, and the random rainfall sequence is used as the boundary condition. The water content field and pore water pressure field are solved in the differentiable computational diagram. S4: Based on the water content field, the cohesion and internal friction angle of the soil are calculated using a water content-dependent shear strength degradation model. S5: Based on the principle of limit equilibrium, the slope safety factor is calculated in the neural network calculation diagram according to the pore water pressure field, soil cohesion and internal friction angle, and the stability is judged. S6: Construct a landslide probability prediction neural network with embedded physical information. The slope environmental characteristics data, water content field, pore water pressure field, soil cohesion and internal friction angle, and slope safety factor are used as inputs, and the landslide probability is used as the output. The network is trained using a joint loss function that includes data-driven loss, infiltration physical constraint loss, and mechanical constraint loss. The Richards equation, shear strength degradation model, and safety factor calculation are embedded in the forward propagation calculation graph of the neural network, so that the physical equations participate in the gradient backpropagation process of network training. S7: Input the multiple sets of rainfall sequences generated in step S2 into the trained landslide probability prediction neural network to obtain multiple landslide probability values, calculate the average landslide probability, maximum landslide probability and exceedance probability, and output a spatial distribution risk map at the regional scale.

2. The method for predicting the probability of rainfall-induced landslides according to claim 1, characterized in that, Step S2 specifically includes: Each rainfall event is defined as a triple containing rainfall intensity, duration, and interval. A joint probability distribution model of rainfall intensity, duration, and interval time was constructed using a parametric model; By using historical rainfall observation data, the parameters of the parameterized model are optimized through maximum likelihood estimation; Construct a conditional probability model to generate rainfall sequences; Statistical consistency constraints are imposed to ensure that the generated rainfall series is consistent with historical observation data in terms of mean and variance; Multiple sets of random rainfall sequences were generated using Monte Carlo sampling to serve as future rainfall scenarios.

3. The method for predicting the probability of rainfall-induced landslides according to claim 2, characterized in that, The Richards equation in step S3 is a one-dimensional vertical Richards equation, expressed as: ； in, This refers to the volumetric moisture content. The unsaturated permeability coefficient, As the matrix potential, Vertical depth t For time; The surface uses flux boundary conditions, which switch to constant head boundary conditions when the rainfall intensity exceeds the saturated permeability coefficient, and the bottom uses free drainage boundary conditions. The relationship between water content and matrix potential was established using the van Genuchten model, and the unsaturated permeability coefficient was established using the Mualem model. The Richards equations were numerically solved using the finite difference method to obtain the water content field and pore water pressure field.

4. The method for predicting the probability of rainfall-induced landslides according to claim 3, characterized in that, The moisture content-dependent shear strength degradation model mentioned in step S4 includes: Cohesion degradation model: ； Degeneracy model of internal friction angle: ； in, The initial cohesion, The initial internal friction angle, The coefficient of decrease in cohesion is denoted as . This is the coefficient for attenuation of the internal friction angle.

5. The method for predicting the probability of rainfall-induced landslides according to claim 4, characterized in that, The slope safety factor in step S5 is calculated using a simplified infinite slope model. ； Where γ is the unit weight of the soil. The depth of the slip surface. The slope angle is... u Pore ​​water pressure; when When the slope is determined to be in an unstable state; The stability of the slope is determined at that time.

6. The method for predicting the probability of rainfall-induced landslides according to claim 5, characterized in that, The landslide probability prediction neural network in step S6 employs a multilayer perceptron network, specifically including: The input layer is used to receive spliced ​​vectors of slope environmental feature data and water content field, pore water pressure field, cohesion, internal friction angle, and slope safety factor; The hidden layers are set to 4 layers, with the number of nodes being 256, 128, 64, and 32 respectively, decreasing in a funnel shape; The output layer has one node that outputs the landslide probability. The hidden layer activation function uses the ReLU function; The output layer activation function uses the Sigmoid function; A Batch Normalization layer and a Dropout layer are inserted between each hidden layer, with the Dropout drop rate set to 0.

3.

7. The method for predicting the probability of rainfall-induced landslides according to claim 6, characterized in that, Online calibration of exceedance probability thresholds is performed using newly added landslide observation events; specifically including: Spatial comparative analysis of the actual landslide areas and the predicted landslide probability results; Statistical analysis of false alarm rate and false negative rate for different time periods; When the false negative rate exceeds a preset threshold, the overshoot probability discrimination boundary is automatically reduced to improve system sensitivity and reduce false negatives. When the false alarm rate exceeds the preset threshold, the overshoot probability discrimination boundary is automatically increased to reduce the false alarm rate. Through continuous iterative updates, the risk warning threshold is dynamically adjusted according to changes in regional climate conditions, geological characteristics, and landslide activity, achieving real-time closed-loop correction between landslide prediction results and actual landslide events.

8. A rainfall-induced landslide probability prediction system, employing the rainfall-induced landslide probability prediction method as described in any one of claims 1-7, characterized in that, include: The data acquisition module is used to acquire and preprocess multi-source historical datasets. The rainfall scenario generation module is used to construct a joint probability distribution model of rainfall events based on historical rainfall observation data, consisting of rainfall intensity, duration, and intermittent time, and generate multiple sets of random rainfall sequences; The infiltration calculation module is used to solve the water content field and pore water pressure field in a differentiable computational graph by using the Richards equation as the infiltration control equation and random rainfall sequence as the boundary condition. The strength degradation calculation module is used to calculate the cohesion and internal friction angle of soil based on the water content field and using a water content-dependent shear strength degradation model. The safety factor calculation module is used to calculate the slope safety factor and determine the stability based on the limit equilibrium principle, according to the pore water pressure field, soil cohesion and internal friction angle in the neural network calculation diagram. The physical constraint training module is used to construct a landslide probability prediction neural network with embedded physical information. It takes slope environmental feature data, water content field, pore water pressure field, soil cohesion and internal friction angle, and slope safety factor as inputs and landslide probability as output. It is trained using a joint loss function that includes data-driven loss, infiltration physical constraint loss and mechanical constraint loss. The risk output module is used to input multiple sets of rainfall sequences into a trained landslide probability prediction neural network to obtain multiple landslide probability values, calculate the average landslide probability, maximum landslide probability and exceedance probability, and output a spatial distribution risk map at the regional scale.

9. The rainfall-induced landslide probability prediction system according to claim 8, characterized in that: The rainfall scenario generation module, infiltration calculation module, intensity degradation calculation module, and slope safety factor calculation module are all uniformly constructed on an end-to-end differentiable computational graph, enabling subsequent landslide prediction errors to be backpropagated and updating the physical parameters and network weights of preceding modules; specifically including: The statistical bias of the rainfall scenario generation module is adjusted by gradient information to adjust the residual weight of the infiltration equation; The moisture field output by the infiltration calculation module affects the updating of intensity degradation parameters; The cohesion and friction angle output by the strength degradation model are optimized and adjusted according to the error gradient; The calculation results of the slope safety factor calculation module are used in the backpropagation of the gradient of the loss function, so that the network weights and physical parameters converge together, thereby realizing the collaborative optimization of each module.

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