A physical residual driving cross-time and space explainable landslide displacement prediction method
Patent Information
- Application Number
- CN202610989247.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-07-03
- Publication Date
- 2026-10-09
AI Technical Summary
[0009]为了解决上述存在的技术问题，本发明提供一种物理残差驱动的跨时空可解释滑坡位移预测方法，主要通过物理约束嵌入、时间因果加权、自适应采样的协同机制实现库岸滑坡位移预测，通过将滑坡位移演化的物理机理与深度学习非线性拟合能力有机融合，解决现有方法物理约束缺失、时间因果不一致、及多尺度适应性差的问题，为库岸滑坡的预测和防灾减灾提供更可靠的技术支持
[0070]1.物理约束嵌入层面。本申请将专门针对阶跃型滑坡构建的经验动力学方程作为物理残差嵌入物理信息神经网络，使网络训练受基于经验动力学方程的物理残差约束，实现了微分方程驱动的物理正则化引导，解决了现有方法物理约束嵌入不充分的问题，模型预测结果具有明确的物理意义。
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Figure CN122885609A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of landslide displacement prediction technology, specifically to a physical residual-driven, spatiotemporally interpretable landslide displacement prediction method. Background Technology
[0002] Reservoir bank landslide displacement prediction is a core quantitative indicator for geological disaster early warning and disaster prevention and mitigation. Conducting research on high-precision and high-reliability landslide displacement prediction has important theoretical significance and engineering application value.
[0003] Currently, methods for predicting landslide displacement along reservoir banks are mainly divided into two categories: physical-driven methods and data-driven methods. Physical-driven methods, based on finite element models (such as GeoStudio) that couple seepage and stress fields, offer strong physical interpretability. However, the spatial variability of hydrogeological parameters and the uncertainty of boundary conditions result in low modeling efficiency and weak generalization ability, limiting their application value in practical engineering. Data-driven methods, through temporal decoupling techniques such as empirical mode decomposition, reconstruct cumulative displacement into trend and periodic terms, and then use machine learning models such as extreme learning machines and support vector machines for sub-term prediction. While these methods have made some progress, as "black box" models, they lack physical constraints and have poor extrapolation capabilities under extreme conditions or data distribution deviations, potentially leading to prediction results that violate the fundamental physical laws of landslide evolution.
[0004] To address the aforementioned issues, the Physics-Informed Neural Network (PINN) offers a novel technical approach for integrating data-driven approaches with physical knowledge by embedding partial differential equations as soft constraints into the loss function. However, existing PINN-based research still suffers from the following shortcomings:
[0005] (1) Insufficient embedding of physical constraints: Existing methods lack a dedicated physical loss function for the displacement evolution mechanism of step-type reservoir bank landslides, resulting in a lack of effective physical guidance during neural network training.
[0006] (2) Ignoring temporal causal consistency: Minimizing the physical residuals simultaneously during model training may violate the temporal evolution order of displacement from the past to the future.
[0007] (3) Lack of adaptive sampling strategy: There is no mechanism for dynamic adjustment of sampling points guided by physical residuals, which leads to uneven application of physical constraints in the critical deformation stage.
[0008] (4) Single time scale: Most existing models are only applicable to a single time scale (such as daily or monthly scale), making it difficult to achieve a unified approach to short-term early warning and medium- and long-term trend assessment. Summary of the Invention
[0009] To address the aforementioned technical problems, this invention provides a physical residual-driven, spatiotemporally interpretable landslide displacement prediction method. It primarily achieves reservoir bank landslide displacement prediction through a collaborative mechanism of physical constraint embedding, temporal causal weighting, and adaptive sampling. By organically integrating the physical mechanism of landslide displacement evolution with the nonlinear fitting capabilities of deep learning, it solves the problems of missing physical constraints, inconsistent temporal causality, and poor multi-scale adaptability in existing methods, providing more reliable technical support for reservoir bank landslide prediction and disaster prevention and mitigation.
[0010] The technical solution adopted in this invention is as follows: A physical residual-driven, spatiotemporally interpretable landslide displacement prediction method is provided, comprising the following steps:
[0011] S01: Data Acquisition: Collect time-series monitoring data on cumulative displacement, rainfall, and reservoir water level in the reservoir bank landslide area; perform data cleaning and normalization; construct the Antecedent Precipitation Index (API) to quantify the cumulative lag effect of rainfall on landslide displacement; based on the rainfall and reservoir water level time-series monitoring data, extract their respective average values, changes, and lag characteristics to construct a multi-dimensional candidate feature set; divide the multi-dimensional candidate feature dataset into training, validation, and test sets in chronological order.
[0012] S02: Optimization of main control feature factors: The Convergent Cross Mapping (CCM) algorithm is used to quantify the causal strength between the multidimensional candidate feature set constructed in step S01 and the cumulative displacement time series data, and features with strong causal relationships are selected as model inputs;
[0013] S03: Construction of Empirical Dynamic Equations: Based on the physical mechanism of landslide displacement evolution, an empirical dynamic equation describing the theoretical evolution rate of step-type landslides is constructed; the equation includes rainfall-reservoir water level coupling driving terms, hydrogeological background terms, and dynamic inertial terms;
[0014] S04: Construction and constraint application of the Physics-Informed Neural Network (PINN): Construct the Physics-Informed Neural Network (PINN), embed the empirical dynamic equations constructed in step S03 as physical residuals into the total loss function, introduce a time-causal weighting mechanism, and apply physical constraints step by step in time order.
[0015] S05: Spatio-Temporal Adaptive Resampling Driven by Physical Residues: Design a Spatio-Temporal Adaptive Resampling (STAR) strategy to dynamically adjust sampling points according to the spatio-temporal distribution of physical residuals, and increase sampling density in areas with large physical residuals;
[0016] S06: Hyperparameter Optimization and Model Training: The Crested Porcupine Optimizer (CPO) algorithm is used to automatically optimize the network structure parameters, loss function weights, and spatiotemporal adaptive resampling strategy hyperparameters of the physical information neural prediction network described in step S04, with the validation set mean square error as the fitness function. The optimal hyperparameters are obtained automatically through the CPO algorithm. Under this hyperparameter configuration, the model is trained using the training set.
[0017] S07: Cumulative Displacement Prediction: Use the trained model to predict the cumulative displacement on the test set.
[0018] Preferably, the method further includes step S08: accuracy evaluation: the accuracy of the cumulative displacement prediction results described in step S07 is evaluated using the coefficient of determination R² and the root mean square error RMSE.
[0019] Preferably, the formula for calculating the anterior rainfall index (API) in step S01 is as follows:
[0020] Formula 1
[0021] In the formula: P t The rainfall amount within the time period [t—Δt,t] is given by k, which is the attenuation coefficient.
[0022] The formula for calculating k is as follows:
[0023] Formula 2
[0024] In the formula: k0 is the reference attenuation coefficient;
[0025] T represents the daily average temperature;
[0026] T ave The average annual temperature;
[0027] F represents the corresponding wind speed;
[0028] F ave The average annual wind speed;
[0029] δ1 and δ2 are the temperature sensitivity index and the wind speed sensitivity index, respectively.
[0030] Preferably, the processing procedure of the convergent cross-mapping algorithm in step S02 is as follows: perform causal analysis on the multidimensional candidate feature set constructed in step S01 and the cumulative displacement time series data, and screen out the features that have a causal driving effect on landslide displacement; specifically, the feature with the strongest causal relationship to the reservoir water level time series monitoring data is used as the sole input of the reservoir water level forcing term H(t) in the rainfall-reservoir water level coupling driving term in the empirical dynamic equation in step S03; the remaining features together with the previous rainfall index API form the input feature set of the subsequent data driving branch.
[0031] Preferably, the calculation formula for the empirical dynamic equation in step S03 is as follows:
[0032] Formula 3
[0033] In the formula: (1) This is a rainfall-reservoir water level coupling driving term;
[0034] k1 and k2 are the weighting coefficients for rainfall and reservoir water level, respectively; R(t) is the API value of the previous rainfall index; H(t) is the reservoir water level forcing term after convergent cross-mapping screening;
[0035] (2) This refers to the hydrogeological background item;
[0036] k3 is the weighting coefficient; S is the landslide slope; L is the permeability coefficient;
[0037] (3) For dynamic inertia;
[0038] k4 is the dynamic inertia coefficient; The predicted displacement acceleration is obtained through automatic differentiation.
[0039] Preferably, the formula for calculating the total loss function L in step S04 is as follows:
[0040] Formula 4
[0041] In the formula: λ ic The weight hyperparameters for the initial conditional loss;
[0042] λ PDE The weighting hyperparameters for the physical residual loss;
[0043] λ inst The weighted hyperparameters for the safety constraint loss;
[0044] L ic For data fitting loss;
[0045] L inst Losses are constrained by a safety upper limit;
[0046] L PDE This refers to the physical residual loss.
[0047] Preferably, the L PDE It is constructed as a form with time-causal weighting:
[0048] Formula 5
[0049] In the formula: J is the number of intervals in the time domain;
[0050] This represents the local physical loss in the j-th interval;
[0051] This represents the summation of all weighted local physical residual losses over the first to the Jth intervals;
[0052] J represents the total number of intervals in the time domain;
[0053] w j For time-based causal weights;
[0054] w j The calculation formula is as follows:
[0055]
[0056] In the formula: For causal parameters;
[0057] This represents the local physical loss in the m-th interval;
[0058] m is the index of the interval less than j.
[0059] Preferably, the spatiotemporal adaptive resampling strategy described in step S05 is implemented as follows:
[0060] Step S051: Divide each time interval into a boundary region and an inner region;
[0061] Step S052: Calculate the sampling probability of each candidate sampling point based on the absolute value of the physical residual;
[0062] Step S053: Assign higher sampling probabilities to regions with large physical residuals to achieve spatial adaptation of sampling.
[0063] Preferably, the sampling probability calculation formula in step S053 is as follows:
[0064] Formula 7
[0065] In the formula: |R PDE(p)| represents the absolute value of the physical residual at point p;
[0066] K is the sampling exponent. When K=0, it is uniform sampling. When K>0, it tends to be a region with high residual.
[0067] To prevent a small constant from having a zero residual probability;
[0068] C represents the set of candidate sampling points.
[0069] Compared with the prior art, the present invention has the following beneficial effects:
[0070] 1. Physical constraint embedding level. This application embeds the empirical dynamic equations specifically constructed for step landslides as physical residuals into the physical information neural network, so that the network training is constrained by the physical residuals based on the empirical dynamic equations. This realizes physical regularization guidance driven by differential equations, solves the problem of insufficient physical constraint embedding in existing methods, and the model prediction results have clear physical meaning.
[0071] 2. Temporal Causality Consistency Level. This application introduces a temporal causal weighting mechanism, which forces the physical residuals to be minimized sequentially along the temporal order of displacement evolution. This ensures that the physical constraints strictly follow the forward evolution order of displacement from the past to the future, solving the problems of existing methods neglecting temporal causal consistency and the possibility that simultaneous minimization of physical residuals may violate the natural order of displacement evolution. This effectively prevents violations of physical consistency.
[0072] 3. Training efficiency and prediction accuracy. This application designs a physical residual-driven spatiotemporal adaptive resampling (STAR) strategy, which dynamically adjusts the sampling points according to the physical residual distribution, enabling the model to automatically focus on regions where physical constraints are severely violated. This solves the problems of existing methods lacking a physical residual-guided adaptive sampling strategy and uneven implementation of physical constraints in key deformation stages. It achieves efficient allocation of computational resources, suppresses the risk of overfitting, and significantly improves the prediction accuracy of the model in key stages such as rapid displacement deformation.
[0073] 4. Adaptability across time scales. The CPO-STAR-PINN framework proposed in this application, through a unified physical constraint architecture, is applicable to both daily-scale (short-term early warning) and monthly-scale (medium- to long-term trend assessment) prediction tasks. This solves the problem that most existing methods are only applicable to a single time scale and are difficult to unify short-term early warning and medium- to long-term trend assessment. It provides a unified technical solution with both high accuracy and strong generalization for full-cycle early warning of reservoir bank landslides.
[0074] In summary, this application systematically solves the problems of missing physical constraints, inconsistent temporal causality, and poor multi-scale adaptability of existing methods through a three-level collaborative mechanism of "physical residual embedding - temporal causal weighting - adaptive resampling", which significantly improves the accuracy, generalization ability and physical interpretability of displacement prediction for step-type reservoir bank landslides. Attached Figure Description
[0075] Figure 1 A graph showing the cumulative displacement, reservoir water level, and rainfall data for monitoring point XP02;
[0076] Figure 2 This is a graph showing the predicted cumulative displacement of monitoring point XP02 after adopting the method of this application;
[0077] Figure 3 A graph showing the cumulative displacement, reservoir water level, and rainfall data for monitoring point ZG111;
[0078] Figure 4 The image shows the predicted cumulative displacement of monitoring point ZG111 after adopting the method of this application. Detailed Implementation
[0079] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the present invention will be further described in detail below with reference to the specific accompanying drawings.
[0080] This invention provides a physical residual-driven method for predicting landslide displacement across time and space that can be interpreted, comprising the following steps:
[0081] S01: Data Acquisition: Collect time-series monitoring data of displacement, rainfall, and reservoir water level from the Global Navigation Satellite System in the reservoir bank landslide area. Obtain cumulative displacement time-series data based on the displacement time-series monitoring data. Construct an API for the previous rainfall index to quantify the cumulative lag effect of rainfall on landslide displacement. Based on the rainfall time-series monitoring data and the reservoir water level time-series monitoring data, extract their respective average values, changes, and lag characteristics to construct a multi-dimensional candidate feature set. Divide the multi-dimensional candidate feature dataset into a training set, a validation set, and a test set in chronological order.
[0082] The API calculation formula is as follows:
[0083] Formula 1
[0084] In the formula: P t The rainfall amount within the time period [t—Δt,t] is given by k, which is the attenuation coefficient.
[0085] The formula for calculating k is as follows:
[0086] Formula 2
[0087] In the formula: k0 is the reference attenuation coefficient;
[0088] T represents the daily average temperature;
[0089] T ave The average annual temperature;
[0090] F represents the corresponding wind speed;
[0091] F ave The average annual wind speed;
[0092] δ1 and δ2 are the temperature sensitivity index and the wind speed sensitivity index, respectively.
[0093] S02: Optimization of Key Controlling Feature Factors: The Converging Cross-Mapping Algorithm [CCM] is used to quantify the causal strength between the multidimensional candidate feature set constructed in step S01 and the cumulative displacement time series data, and to select features with strong causal relationships as model inputs. The processing of the Converging Cross-Mapping Algorithm is as follows: causal analysis is performed on the multidimensional candidate feature set constructed in step S01 and the cumulative displacement time series data to select features that have a causal driving effect on landslide displacement. Specifically, the feature with the strongest causal relationship to the reservoir water level time series monitoring data is used as the sole input to the reservoir water level forcing term H(t) in the rainfall-reservoir water level coupling driving term in the empirical dynamic equation described in step S03. The remaining features, together with the previous rainfall index API, form the input feature set of the subsequent data-driven branch.
[0094] S03: Construction of Empirical Dynamic Equations: Based on the physical mechanism of landslide displacement evolution, an empirical dynamic equation describing the theoretical evolution rate of step-type landslides is constructed. This equation includes a rainfall-reservoir water level coupling driving term, a hydrogeological background term, and a dynamic inertial term. The calculation formula of the empirical dynamic equation is as follows:
[0095] Formula 3
[0096] In the formula: (1) This is a rainfall-reservoir water level coupling driving term;
[0097] k1 and k2 are the weighting coefficients for rainfall and reservoir water level, respectively; R(t) is the API value of the previous rainfall index; H(t) is the reservoir water level forcing term after convergent cross-mapping screening;
[0098] (2) This refers to the hydrogeological background item;
[0099] k3 is the weighting coefficient; S is the landslide slope; L is the permeability coefficient;
[0100] (3) For dynamic inertia;
[0101] k4 is the dynamic inertia coefficient; The predicted displacement acceleration is obtained through automatic differentiation.
[0102] S04: Construction and Constraint Application of Physical Information Neural Network: Construct a physical information neural prediction network, embed the empirical dynamic equation constructed in step S03 as a physical residual term into the total loss function, introduce a time-causal weighting mechanism, and apply physical constraints step by step in time sequence;
[0103] The formula for calculating the total loss function L is as follows:
[0104] Formula 4
[0105] In the formula: λ ic The weight hyperparameters for the initial conditional loss;
[0106] λ PDE The weighting hyperparameters for the physical residual loss;
[0107] λ inst The weighted hyperparameters for the safety constraint loss;
[0108] L ic For data fitting loss;
[0109] L inst Losses are constrained by a safety upper limit;
[0110] L PDE This refers to the physical residual loss.
[0111] Among them, L PDE It is constructed as a form with time-causal weighting:
[0112] Formula 5
[0113] In the formula: J is the number of intervals in the time domain;
[0114] This represents the local physical loss in the j-th interval;
[0115] This represents the summation of all weighted local physical residual losses over the first to the Jth intervals;
[0116] J represents the total number of intervals in the time domain;
[0117] w j For time-based causal weights;
[0118] w j The calculation formula is as follows:
[0119]
[0120] In the formula: For causal parameters;
[0121] This represents the local physical loss in the m-th interval;
[0122] m is the index of the interval less than j.
[0123] S05: Spatiotemporal adaptive resampling driven by physical residuals: Design a spatiotemporal adaptive resampling [STAR] strategy to dynamically adjust sampling points according to the spatiotemporal distribution of physical residuals and increase sampling density in areas with large physical residuals;
[0124] The spatiotemporal adaptive resampling strategy is implemented as follows:
[0125] Step S051: Divide each time interval into a boundary region and an inner region;
[0126] Step S052: Calculate the sampling probability of each candidate sampling point based on the absolute value of the physical residual;
[0127] Step S053: Assign higher sampling probabilities to regions with large physical residuals to achieve spatial adaptive sampling. The sampling probability calculation formula is as follows:
[0128] Formula 7
[0129] In the formula: |R PDE (p)| represents the absolute value of the physical residual at point p;
[0130] K is the sampling exponent. When K=0, it is uniform sampling. When K>0, it tends to be a region with high residual.
[0131] To prevent a small constant from having a zero residual probability;
[0132] C represents the set of candidate sampling points.
[0133] S06: Hyperparameter optimization and model training: The CPO algorithm is used to automatically optimize the network structure parameters, loss function weights and spatiotemporal adaptive resampling strategy hyperparameters of the physical information neural prediction network described in step S04, and the verification set mean square error as the fitness function. The optimal hyperparameters are obtained automatically by the CPO algorithm. Under this hyperparameter configuration, the model is trained using the training set.
[0134] S07: Cumulative Displacement Prediction: Predict cumulative displacement on the test set using the trained model;
[0135] S08: Accuracy Evaluation: The accuracy of the cumulative displacement prediction results described in step S07 is evaluated using the coefficient of determination R² and the root mean square error RMSE.
[0136] Example 1: Taking the Xinpu landslide in the Three Gorges as an example (monitoring point: XP02)
[0137] (1) The Xinpu landslide in the Three Gorges area is located on the south bank of the Yangtze River in Fengjie County, Chongqing, about 182 km from the Three Gorges Dam. It is a super-large landslide group with bedding-micro-cutting layers. The overall length of the landslide is about 2.00 km, the relative height difference is 634.40 m, and the slope is 15°-20°. High-precision GNSS surface displacement monitoring points and rain gauges and other real-time monitoring systems have been deployed in the Xinpu landslide area. In this embodiment, the key monitoring point XP02 of the Xinpu landslide is selected, and the daily-scale monitoring data from January 1, 2020 to January 1, 2024 are used as the research object.
[0138] like Figure 1 As shown, S01: is a time-series monitoring data chart of cumulative displacement, rainfall, and reservoir water level of the newly landslide. Figure 1 As can be seen, under the combined effects of reservoir water level fluctuations and rainfall, the cumulative displacement of the reservoir bank landslide exhibits a clear step-like increase. After outlier removal and normalization, the dataset was divided into training, validation, and test sets according to time sequence. The training set data was used for model training, the validation set data was used for validating model prediction results, and the test set data was used for model testing.
[0139] Based on the time-series monitoring data of rainfall and reservoir water level, a multi-dimensional candidate feature set is constructed, specifically including the following categories:
[0140] (1) Rainfall-related characteristics: previous rainfall index [API], daily rainfall, average rainfall of the previous n days, rainfall variation of the previous n days, and rainfall of the next n days;
[0141] (2) Reservoir water level related characteristics: daily reservoir water level, average reservoir water level of the previous n days, intraday reservoir water level change of the previous n days, and reservoir water level of the next n days.
[0142] S02: Based on this, the convergent cross-mapping algorithm [CCM] is used to filter the feature set composed of features other than the previous rainfall index API, and the reservoir water level feature that shows the strongest causal strength is used as the sole input of the reservoir water level forcing term H(t) in the subsequent constructed empirical dynamic equation. The final results of the best input feature selection are shown in Table 1.
[0143] XP02 API Average reservoir water level of the previous 5 days, average reservoir water level of the previous 10 days, and reservoir water level lag of the previous 15 days.
[0144] (Table 1)
[0145] S03: Construct the empirical dynamic equation for a step-type landslide. This equation consists of three terms: a rainfall-reservoir level coupling driving term, a hydrogeological background term, and a dynamic inertial term. Refer to Formula 3 for details.
[0146] S04: The empirical dynamic equation is embedded as a physical residual constraint into the total loss function of the neural network, and a time-causal weighting strategy is introduced.
[0147] S05: The entire time domain is divided into multiple continuous intervals, and causal weights are assigned to the local physical loss of each interval. Based on this, spatiotemporal adaptive resampling driven by physical residuals is performed, enabling the model to focus limited computational resources on key spatiotemporal regions where physical constraints are difficult to meet.
[0148] S06: Hyperparameter optimization is performed using the Crowned Porcupine optimization algorithm. Under this hyperparameter configuration, the model is trained using the training set.
[0149] S07: Use the trained model to predict cumulative displacement on the test set.
[0150] S08: Finally, based on the actual value of cumulative displacement and the predicted value of cumulative displacement, the coefficient of determination R2 and the root mean square error RMSE are calculated to evaluate the accuracy of the cumulative displacement prediction results.
[0151] like Figure 2 The figure shows the cumulative displacement prediction results for monitoring point XP02. Monitoring point XP02 uses daily monitoring data from January 1, 2020 to January 1, 2024. The cumulative displacement prediction is performed using a physical residual-driven, spatiotemporally interpretable landslide displacement prediction method proposed in this application. Figure 2 It can be seen that after adopting the method described in this application, the prediction accuracy of the cumulative displacement of monitoring point XP02 is greatly improved. The calculated determination coefficient R² of the cumulative displacement of monitoring point XP02 is 0.99, and the root mean square error RMSE is 3.84 mm.
[0152] Comparative Example 1:
[0153] To verify the effectiveness of the method described in this application, comparative experiments were conducted at the XP02 monitoring point using Transformer and BiGRU models driven purely by data.
[0154] This application method 0.99 3.84 Transformer 0.98 25.91 BiGRU 0.99 14.94
[0155] (Table 2)
[0156] Compared with the Transformer and BiGRU methods, the determination coefficient R² of the method in this application can remain basically unchanged, while the root mean square error RMSE is reduced by approximately 85.18% and 74.30%, respectively.
[0157] Example 2: Taking the Bazimen landslide in the Three Gorges as an example (monitoring point: ZG111)
[0158] (2) The Bazimen landslide of the Three Gorges is located on the right bank of the Xiangxi River, a tributary of the Yangtze River, 38 km from the Three Gorges Dam site. The main sliding direction is S60°E, the slope is 10°-30°, and the total volume of the landslide is about 4×10. 9 m³. In this embodiment, the landslide deformation monitoring point ZG111 was selected, and the monthly monitoring data from February 1, 2004 to February 1, 2010 were used as the research object.
[0159] like Figure 3 As shown, S01: is a time-series monitoring data chart of cumulative displacement, rainfall, and reservoir water level of the Bazimen landslide. Figure 3 As can be seen, under the combined effects of reservoir water level fluctuations and rainfall, the cumulative displacement of the reservoir bank landslide exhibits a clear step-like increase. After outlier removal and normalization, the dataset was divided into training, validation, and test sets according to time sequence. The training set data was used for model training, the validation set data was used for validating model prediction results, and the test set data was used for model testing.
[0160] Similarly, based on the aforementioned rainfall time-series monitoring data and reservoir water level time-series monitoring data, a multi-dimensional candidate feature set is constructed, specifically including the following categories:
[0161] (1) Rainfall-related characteristics: the previous rainfall index [API], the current month's rainfall, the average rainfall of the previous n months, the change in rainfall within the previous n months, and the rainfall of the lagged n months;
[0162] (2) Reservoir water level related characteristics: monthly reservoir water level, average reservoir water level of the previous n months, reservoir water level change in the previous n months, and reservoir water level of the next n months.
[0163] S02: Based on this, the convergent cross-mapping algorithm [CCM] is used to filter the feature set composed of features other than the previous rainfall index API, and the reservoir water level feature with the strongest causal strength is used as the sole input of the reservoir water level forcing term H(t) in the subsequent constructed empirical dynamic equation. The final results of the best input feature selection are shown in Table 3.
[0164] ZG111 API, average rainfall in the first 5 months, average rainfall in the first 7 months, average rainfall in the first 8 months Average reservoir water level in the first four months
[0165] (Table 3)
[0166] S03: Construct the empirical dynamic equation for a step-type landslide. This equation consists of three terms: a rainfall-reservoir level coupling driving term, a hydrogeological background term, and a dynamic inertial term. Refer to Formula 3 for details.
[0167] S04: The empirical dynamic equation is embedded as a physical residual constraint into the total loss function of the neural network, and a time-causal weighting strategy is introduced.
[0168] S05: The entire time domain is divided into multiple continuous intervals, and causal weights are assigned to the local physical loss of each interval. Based on this, spatiotemporal adaptive resampling driven by physical residuals is performed, enabling the model to focus limited computational resources on key spatiotemporal regions where physical constraints are difficult to meet.
[0169] S06: Hyperparameter optimization is performed using the Crowned Porcupine optimization algorithm. Under this hyperparameter configuration, the model is trained using the training set.
[0170] S07: Use the trained model to predict cumulative displacement on the test set.
[0171] S08: Finally, based on the actual value of cumulative displacement and the predicted value of cumulative displacement, the coefficient of determination R2 and the root mean square error RMSE are calculated to evaluate the accuracy of the cumulative displacement prediction results.
[0172] like Figure 4 The figure shows the cumulative displacement prediction results for monitoring point ZG111. Monthly monitoring data from February 1, 2004 to February 1, 2010 were selected for monitoring point ZG111. The cumulative displacement was predicted using a physical residual-driven, spatiotemporally interpretable landslide displacement prediction method proposed in this application. Figure 4 It can be seen that after adopting the method described in this application, the prediction accuracy of the cumulative displacement of monitoring point ZG111 is greatly improved. The calculated coefficient of determination R² of the cumulative displacement of monitoring point ZG111 is 0.99, and the root mean square error RMSE is 8.55 mm.
[0173] Comparative Example 2:
[0174] To verify the superiority of the method proposed in this application, comparative experiments were conducted at the ZG111 monitoring point using the Transformer and BIGRU models, which are driven purely by data.
[0175] This application method 0.99 8.55 Transformer 0.98 39.17 BIGRU 0.97 47.38
[0176] (Table 4)
[0177] Compared with the Transformer and BiGRU methods, the determination coefficient R² of the method in this application can remain basically unchanged, while the root mean square error RMSE is reduced by approximately 78.17% and 77.86%, respectively.
[0178] In summary, the comparison results between the two embodiments and the Transformer and BiGRU methods show that: in terms of physical constraint embedding, this application uses the empirical dynamic equation as the total loss function for physical residual embedding, giving the model prediction results a clear physical meaning. Compared with the pure data-driven method, the RMSE is significantly reduced while keeping R² essentially unchanged, indicating that physical regularization constraints effectively improve prediction accuracy. In terms of temporal causal consistency, the temporal causal weighting strategy forces the network to learn along the positive temporal sequence of displacement evolution, preventing violations of physical consistency. In terms of training efficiency and prediction accuracy, the spatiotemporal adaptive resampling mechanism driven by physical residuals enables the model to automatically focus on regions with weak physical constraints, achieving efficient allocation of computational resources. In terms of cross-timescale adaptability, the CPO-STAR-PINN framework proposed in this application can be applied to both daily and monthly scale prediction tasks without changing the core network architecture. This demonstrates that the present application achieves high-precision, strong generalization, and multi-timescale adaptation prediction results for step-type reservoir bank landslide displacements through the synergistic cooperation of physical residual embedding, temporal causal weighting, and spatiotemporal adaptive resampling, respectively complementing each other in terms of the physical rationality of the prediction, the logicality of temporal learning, and the sampling efficiency.
[0179] The above description is only a preferred embodiment of the present invention, and the scope of protection of the present invention is not limited thereto. For those skilled in the art, any equivalent substitutions or obvious modifications made based on the content and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A physical residual-driven method for predicting landslide displacement across time and space, characterized in that: Includes the following steps: S01: Data Acquisition: Collect time-series monitoring data on cumulative displacement, rainfall, and reservoir water level in the reservoir bank landslide area; complete data cleaning and normalization; construct the Anterior Rainfall Index (API) to quantify the cumulative lag effect of rainfall on landslide displacement; Based on the time-series monitoring data of rainfall and reservoir water level, their respective average values, changes, and lag characteristics are extracted to construct a multi-dimensional candidate feature set; the multi-dimensional candidate feature dataset is then divided into a training set, a validation set, and a test set according to time order. S02: Optimization of main control feature factors: The convergent cross-mapping algorithm is used to quantify the causal strength between the multidimensional candidate feature set constructed in step S01 and the cumulative displacement time series data, and features with strong causal relationship are selected as model inputs. S03: Construction of Empirical Dynamic Equations: Based on the physical mechanism of landslide displacement evolution, an empirical dynamic equation describing the theoretical evolution rate of step-type landslides is constructed; the equation includes rainfall-reservoir water level coupling driving terms, hydrogeological background terms, and dynamic inertial terms; S04: Construction and Constraint Application of Physical Information Neural Network: Construct a physical information neural prediction network, embed the empirical dynamic equation constructed in step S03 as a physical residual term into the total loss function, introduce a time-causal weighting mechanism, and apply physical constraints step by step in time sequence; S05: Spatiotemporal adaptive resampling driven by physical residuals: Design a spatiotemporal adaptive resampling strategy to dynamically adjust the sampling points according to the spatiotemporal distribution of physical residuals and increase the sampling density in areas with large physical residuals. S06: Hyperparameter optimization and model training: The hyperparameters of the physical information neural prediction network described in step S04, the loss function weights, and the spatiotemporal adaptive resampling strategy described in step S05 are automatically optimized using the hog optima algorithm. The mean square error of the validation set is used as the fitness function. The optimal hyperparameters are obtained automatically through the hog optima algorithm. Under this hyperparameter configuration, the model is trained using the training set. S07: Cumulative Displacement Prediction: Use the trained model to predict the cumulative displacement on the test set.
2. The physical residual-driven, spatiotemporally interpretable landslide displacement prediction method according to claim 1, characterized in that: It also includes the following steps: S08: Accuracy Evaluation: The accuracy of the cumulative displacement prediction results described in step S07 is evaluated using the coefficient of determination R² and the root mean square error RMSE.
3. The physical residual-driven, spatiotemporally interpretable landslide displacement prediction method according to claim 1, characterized in that: The formula for calculating the Apparent Rainfall Index (API) in step S01 is as follows: Official 1 In the formula: P t The rainfall amount within the time period [t—Δt,t] is given by k, which is the attenuation coefficient. The formula for calculating k is as follows: Official 2 In the formula: k0 is the reference attenuation coefficient; T represents the daily average temperature; T ave The average annual temperature; F represents the corresponding wind speed; F ave The average annual wind speed; δ1 and δ2 are the temperature sensitivity index and the wind speed sensitivity index, respectively.
4. The physical residual-driven, spatiotemporally interpretable landslide displacement prediction method according to claim 1, characterized in that: The processing procedure of the convergent cross-mapping algorithm in step S02 is as follows: perform causal analysis on the multidimensional candidate feature set constructed in step S01 and the cumulative displacement time series data, and screen out the features that have a causal driving effect on landslide displacement; specifically, the feature with the strongest causal relationship with the reservoir water level time series monitoring data is used as the sole input of the reservoir water level forcing term H(t) in the rainfall-reservoir water level coupling driving term in the empirical dynamic equation in step S03; The remaining features, together with the previous rainfall index API, form the input feature set for the subsequent data-driven branch.
5. The physical residual-driven, spatiotemporally interpretable landslide displacement prediction method according to claim 1, characterized in that: The calculation formula for the empirical dynamic equation mentioned in step S03 is as follows: Official 3 In the formula: (1) This is a rainfall-reservoir water level coupling driving term; k1 and k2 are the weighting coefficients for rainfall and reservoir water level, respectively; R(t) is the API value of the previous rainfall index; H(t) is the reservoir water level forcing term after convergent cross-mapping screening; (2) This refers to the hydrogeological background item; k3 is the weighting coefficient; S is the landslide slope; L is the permeability coefficient; (3) For dynamic inertia; k4 is the dynamic inertia coefficient; The predicted displacement acceleration is obtained through automatic differentiation.
6. The physical residual-driven, spatiotemporally interpretable landslide displacement prediction method according to claim 1, characterized in that: The formula for calculating the total loss function L mentioned in step S04 is as follows: Official 4 In the formula: λ ic The weight hyperparameters for the initial conditional loss; λ PDE The weighting hyperparameters for the physical residual loss; λ inst The weighted hyperparameters for the safety constraint loss; L ic For data fitting loss; L inst Losses are constrained by a safety upper limit; L PDE This refers to the physical residual loss.
7. The physical residual-driven, spatiotemporally interpretable landslide displacement prediction method according to claim 6, characterized in that: The L PDE It is constructed as a form with time-causal weighting: Official 5 In the formula: J is the number of intervals in the time domain; This represents the local physical loss in the j-th interval; This represents the summation of all weighted local physical residual losses over the first to the Jth intervals; J represents the total number of intervals in the time domain; w j For time-based causal weights; w j The calculation formula is as follows: Official 6 In the formula: For causal parameters; This represents the local physical loss in the m-th interval; m is the index of the interval less than j.
8. The physical residual-driven, spatiotemporally interpretable landslide displacement prediction method according to claim 1, characterized in that: The spatiotemporal adaptive resampling strategy described in step S05 is implemented as follows: Step S051: Divide each time interval into a boundary region and an inner region; Step S052: Calculate the sampling probability of each candidate sampling point based on the absolute value of the physical residual; Step S053: Assign higher sampling probabilities to regions with large physical residuals to achieve spatial adaptation of sampling.
9. The physical residual-driven, spatiotemporally interpretable landslide displacement prediction method according to claim 8, characterized in that: The sampling probability calculation formula mentioned in step S053 is as follows: Official 7 In the formula: |R PDE (p)| represents the absolute value of the physical residual at point p; K is the sampling exponent. When K=0, it is uniform sampling. When K>0, it tends to be a region with high residual. To prevent a small constant from having a zero residual probability; C represents the set of candidate sampling points.