Data and physics dual-drive balance weight type road shoulder retaining wall soil pressure prediction method

Abstract

The invention discloses a data and physics dual-drive balance weight type road shoulder retaining wall soil pressure prediction method, which comprises the following steps: firstly, constructing a self-adaptive finite element limit analysis reference model to obtain wall back soil pressure and a fracture surface form, and then extracting a physical rule in combination with a classic soil pressure theory and converting the physical rule into a differentiable mathematical constraint; generating a multi-working-condition structured data set through Latin hypercube sampling in combination with the reference model; and then establishing a physical information neural network model fused with physical constraints, screening out an optimal model through hyper-parameter optimization and batch training, and finally loading the model to realize soil pressure prediction. According to the method, physical constraints are embedded into the neural network, dependence on measured data is reduced, physical consistency is still kept in a data sparse region, soil pressure and fracture surface dip angle parameters of all parts of the wall back can be synchronously output, prediction precision and generalization ability are greatly improved, a comprehensive basis is provided for fine design of the retaining wall, and the rapid design requirement of a project is met.

Description

Technical Field

[0001] This invention relates to the field of earth pressure calculation technology for retaining structures, specifically a method for predicting earth pressure on a counterweight shoulder retaining wall driven by both data and physical factors. Background Technology

[0002] Counterweight shoulder retaining walls are core retaining structures in highway and railway subgrade engineering. They mainly consist of three parts: an upper wall, a counterweight platform, and a lower wall. The upper wall is designed with an upward inclination to achieve load unloading, the counterweight platform is a horizontal load-bearing structure to transfer and diffuse stress, and the lower wall is a vertical or slightly inclined structure to bear the main earth pressure load. The whole structure forms a three-part mechanical structure system of "upper wall unloading, counterweight platform transmitting force, and lower wall bearing the load," which effectively reduces the earth pressure behind the wall and improves the overall stability of the structure. It is widely used in complex geological conditions such as mountain roadbeds and slope protection. Accurate determination of the earth pressure behind the wall (including the earth pressure of the upper wall, lower wall, and counterweight platform) and the parameters of the rupture surface is crucial to ensuring the safety and economy of retaining wall design. It directly determines the rationality of the retaining wall structural dimensions and reinforcement design. Therefore, conducting research on accurate prediction of earth pressure behind the wall has significant practical engineering implications. Existing methods for calculating earth pressure have significant shortcomings and are difficult to adapt to engineering design requirements: Traditional analytical methods based on standards rely on simplified assumptions such as "planar rupture surface" and "linear earth pressure distribution," neglecting the mechanical coupling effect of the upper and lower walls of a counterweight structure, the nonlinear characteristics of the soil, and complex boundary conditions. This easily leads to underestimation of earth pressure on the upper wall and overestimation of earth pressure on the lower wall, and it cannot accurately depict the morphology of the second rupture surface of the upper wall, resulting in significant deviations in calculation results. While pure numerical simulation methods can better simulate the complex mechanical behavior of soil and retaining walls, single-condition calculations are time-consuming and require professional technicians to complete tasks such as mesh generation and parameter adjustment, resulting in high computational costs and failing to meet the efficiency requirements of rapid engineering design and multi-scheme comparison. At the same time, measured earth pressure data in the field of geotechnical engineering is scarce and costly to obtain. Traditional data-driven methods, due to their reliance on massive amounts of high-quality measured data, have poor generalization ability and are prone to producing results that violate physical laws in data-sparse regions. Therefore, developing an earth pressure prediction method with low dependence on measured data, high prediction accuracy, and efficient and convenient calculation has become an urgent need for the intelligent and refined design of counterweight shoulder retaining walls.

[0003] Currently, there are three main methods for calculating earth pressure on load-bearing retaining walls with shoulders, all of which have significant technical defects: Firstly, traditional analytical methods (such as Coulomb's earth pressure theory and Rankine's theory) are based on simplified assumptions such as "planar rupture surface" and "linear earth pressure distribution," which ignore the mechanical coupling between the upper and lower walls of the counterweight structure, the nonlinear characteristics of the soil, and complex boundary conditions. This leads to a general underestimation of the earth pressure on the upper wall and an overestimation of the earth pressure on the lower wall. Furthermore, they cannot accurately capture the morphology of the second rupture surface of the upper wall, making it difficult to meet the needs of modern engineering's refined design. Secondly, while pure numerical simulation methods (such as the finite element method (FEM) and finite element limit analysis (FELA) can simulate complex mechanical behavior, their computational cost is high—a single-condition calculation can take 10-30 minutes, and they require a high level of professional knowledge and practical experience from the operators. Typically, personnel with relevant experience in geotechnical engineering numerical simulation are needed to complete mesh generation and parameter debugging. Mesh generation needs to be reasonably designed in combination with the stress concentration areas of the soil and the characteristics of the structural boundaries, while parameter debugging needs to be repeatedly verified in combination with the constitutive properties of the soil, failure criteria, and actual engineering conditions. If relevant experience is lacking, improper operation can easily lead to deviations in the calculation results, making it difficult to meet the accuracy requirements of engineering design. This also limits its widespread application in ordinary engineering design and cannot meet the efficiency requirements of rapid engineering design and multi-scheme comparison. Third, there are data-driven and traditional hybrid modeling methods. Pure data-driven methods (such as BP neural networks and LSTM) rely on massive amounts of high-quality measured data. However, measured earth pressure data in geotechnical engineering is scarce and costly to obtain, resulting in poor model generalization ability. In data-sparse regions, the model is prone to outputting results that violate physical laws (such as earth pressure decreasing with wall height and the angle of the rupture surface exceeding the geometrically reasonable range). Some traditional hybrid modeling methods adopt a technical route of "combining mechanism and data in segments", which requires inverting intermediate parameters through mechanism models. This fails to achieve a deep integration of physical laws and neural networks. In complex boundary or data-scarce scenarios, there are still problems of insufficient prediction rationality and poor physical consistency.

[0004] Physics-Informed Neural Networks (PINN), as an emerging hybrid modeling technique, addresses the core deficiency of "physically unconstrained" pure data-driven models by embedding physical laws into neural network training in the form of partial differential equations (PDEs). It has been successfully applied in fields such as fluid mechanics and solid mechanics. However, in geotechnical engineering, PINN has not yet been specifically applied to predict earth pressure in load-bearing retaining walls. Existing PINN applications mostly involve "segmented combination of physical laws," lacking explicit, differentiable, and deep embedding designs, and do not simultaneously output earth pressure and rupture surface parameters, failing to meet the dual requirements of engineering design for "quantitative results + physical mechanisms."

[0005] Furthermore, the calculation of earth pressure on counterweight retaining walls faces unique challenges: the presence of a second rupture surface on the upper wall significantly affects stress distribution, which traditional methods struggle to accurately characterize; the stress diffusion effect of the counterweight platform needs to be analyzed in conjunction with the soil arching effect, and existing models lack targeted physical constraint design. Therefore, there is an urgent need for a technical solution that integrates "high-precision numerical data generation, explicit physical constraint embedding, and efficient prediction" to address the pain points of existing methods, such as poor physical consistency, high data dependence, low computational efficiency, and incomplete engineering output.

[0006] Based on this, the present invention proposes a technical approach to generate high-quality data through numerical simulation (AFELA) and embed physical constraints into PINN. It generates a multi-condition structural dataset through adaptive finite element limit analysis and embeds the earth pressure balance equation and rupture surface boundary conditions into PINN in the form of differentiable constraints. This enables synchronous and accurate prediction of earth pressure and rupture surface parameters, fills the gap in existing technology, and provides a reliable tool for the intelligent design of counterweight shoulder retaining walls. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention provides a method for predicting earth pressure on a counterweight shoulder retaining wall driven by both data and physics. The aim is to achieve high-precision, high-efficiency earth pressure prediction that conforms to physical laws, while outputting rupture surface parameters to provide a comprehensive basis for engineering design.

[0008] To achieve the above objectives, the present invention provides the following technical solution: a data- and physical dual-driven method for predicting earth pressure on a weighted shoulder retaining wall, comprising the following steps: Step S1: Construct an adaptive finite element limit analysis benchmark model and run the analysis to obtain the distribution of earth pressure on the back of the counterweight shoulder retaining wall and the morphology of the rupture surface under different working conditions. Step S2: Based on the benchmark model running results and combined with earth pressure theory, extract the input parameters of the counterweight shoulder retaining wall structure and backfill material. Relying on Coulomb earth pressure theory and the mechanism of the second rupture surface of the counterweight retaining wall, transform the physical laws of earth pressure calculation into differentiable mathematical constraints. Step S3: Based on the input parameters of the benchmark model, the counterweight shoulder retaining wall structure and the backfill material, determine the range of input parameter values ​​according to the specifications, generate several sets of multi-condition parameters using Latin hypercube sampling, extract the target output parameters through automated modeling and calculation, and construct a structured dataset; Step S4: Construct a data preprocessing module to periodically preprocess the operating parameters in the structured dataset; Step S5: Establish a physical information neural network model, design the network architecture, define a loss function that incorporates differentiable mathematical constraints, and use the Optuna hyperparameter optimization framework for automated tuning; Step S6: Based on the optimized physical information neural network model and the structured dataset preprocessed by the data preprocessing module, perform batch model training and select the optimal physical information neural network model; Step S7: Conduct earth pressure prediction, collect real-time input parameters of the counterweight shoulder retaining wall structure and backfill material, preprocess them through the data preprocessing module and input them into the optimal physical information neural network model, and output the earth pressure prediction results.

[0009] Further, the specific process of step S1 is as follows: Based on the design drawings of the counterweight shoulder retaining wall, establish a two-dimensional adaptive finite element limit analysis model; set the material constitutive model, boundary conditions, and multiplier load conditions to simulate the actual working state; use adaptive mesh technology to refine the mesh in the stress concentration area of ​​the counterweight shoulder retaining wall; run the adaptive finite element limit analysis to obtain the earth pressure distribution and rupture surface morphology of the counterweight shoulder retaining wall; and compare and verify the rationality of the two-dimensional adaptive finite element limit analysis model.

[0010] Furthermore, the specific process of step S2 is as follows: analyze the dimensional sensitivity of the counterweight shoulder retaining wall structure, and determine the total wall height of the counterweight shoulder retaining wall. The back slope angle of the upper wall of the counterweight shoulder retaining wall The back slope angle of the lower wall of a counterweight retaining wall Width of the weighing platform Input parameters for the structure; analyze the fill material and determine the cohesion of the fill. The internal friction angle of the backfill Input parameters for the backfill material; based on Coulomb's earth pressure theory and the mechanism of the second rupture surface of a weighted retaining wall, establish a physical model for earth pressure calculation and extract the earth pressure function. Regarding the inclination angle of the second fracture surface on the wall Inclination angle of the first fracture surface on the wall The extreme value conditions are satisfied and transformed into differentiable constraints; the inclination angle of the second rupture surface of the upper wall is defined. Inclination angle of the first fracture surface on the wall Boundary constraints.

[0011] Further, the specific process of step S3 is as follows: determine the range of input parameter values ​​for the counterweight shoulder retaining wall structure and backfill material; classify the backfill soil into three categories: sand, silt, and clay; based on the backfill soil type and the input parameters of the counterweight shoulder retaining wall structure and backfill material, generate several sets of working condition parameters using Latin hypercube sampling; based on each set of working condition parameters, execute the automated modeling and calculation process by calling automated modeling software combined with the adaptive finite element limit analysis benchmark model; extract the backfill pressure of the counterweight shoulder retaining wall from the calculation results of each set of working condition parameters. Earth pressure behind the wall Earth pressure of the counterweight platform Inclination angle of the second fracture surface on the upper wall and the inclination angle of the first fracture surface on the wall As the target output parameter, construct a structured dataset containing operating condition parameters and corresponding target output parameters.

[0012] Furthermore, the specific process of step S4 is as follows: the data preprocessing module processes the wall back tilt angle in the working condition parameters of the structured dataset. Lower wall back slope angle Calculate the sin and cos values ​​respectively to form an 8-dimensional feature vector. .

[0013] Furthermore, the specific process of step S5 is as follows: Design a neural network model architecture for physical information: The input layer contains 8 nodes, corresponding to 8-dimensional feature vectors. ; The hidden layers contain multiple fully connected layers, using the Tanh activation function and batch normalization; The output layer contains 5 nodes, corresponding to the target output parameter: soil pressure on the wall. Earth pressure behind the wall Earth pressure of the counterweight platform Inclination angle of the second fracture surface on the upper wall and the inclination angle of the first fracture surface on the wall ; The total loss function of the physical information neural network model is defined. This total loss function is obtained by a weighted sum of the data loss term, the physical residual loss term, and the boundary constraint loss term. Each term corresponds to the data fitting weight, the physical constraint weight, and the boundary constraint weight, respectively. The data loss term measures the deviation between the predicted values ​​of the physical information neural network model and the measured label values. The physical residual loss term is calculated using Huber loss, based on the number of sampling points constrained by physical laws, the PDE residual term, the trainable parameters of the model, the partial derivatives of earth pressure, and the threshold parameters. The partial derivatives of earth pressure are numerically solved using the finite difference method. Using the Optuna hyperparameter optimization framework, with the goal of minimizing PDE residuals, and employing Bayesian sampling and pruning strategies, we conducted hyperparameter search for the physical information neural network model. Loss weights are allocated differently based on the training stage of the physical information neural network model.

[0014] Furthermore, the specific process of step S6 is as follows: based on the preprocessed structured dataset, a standardized physical information neural network model training framework is built; based on the optimized physical information neural network model and loss function, multiple batch model trainings are carried out; after training, a multi-dimensional comprehensive scoring system is constructed to quantitatively evaluate and rank all trained models; based on the comprehensive scoring results, the physical information neural network model with the best score is selected.

[0015] A data- and physics-driven system for predicting earth pressure on a load-bearing shoulder retaining wall includes: The adaptive finite element limit analysis module is used to construct an adaptive finite element limit analysis benchmark model and run the analysis to obtain the distribution of earth pressure on the back of the counterweight shoulder retaining wall and the morphology of the rupture surface under different working conditions. The physical knowledge extraction module is used to extract the input parameters of the counterweight shoulder retaining wall structure and backfill material based on the benchmark model running results and combined with earth pressure theory. Relying on Coulomb earth pressure theory and the mechanism of the second rupture surface of the counterweight retaining wall, the physical laws of earth pressure calculation are transformed into differentiable mathematical constraints. The dataset construction module is used to determine the range of input parameter values ​​according to the specifications based on the input parameters of the benchmark model, the counterweight shoulder retaining wall structure and the backfill material, generate several sets of multi-condition parameters using Latin hypercube sampling, extract the target output parameters through automated modeling and calculation, and construct a structured dataset. The parameter optimization module is used to build the data preprocessing module, which performs periodic preprocessing on the operating parameters in the structured dataset. The model optimization module is used to build a physical information neural network model, design the network architecture, define a loss function that incorporates differentiable mathematical constraints, and use the Optuna hyperparameter optimization framework for automated tuning. The model training module is used to perform batch model training and select the optimal physical information neural network model based on the optimized physical information neural network model and the structured dataset preprocessed by the data preprocessing module. The real-time prediction module is used to predict earth pressure. It collects real-time input parameters of the counterweight shoulder retaining wall structure and backfill material. After preprocessing by the data preprocessing module, the data is input into the optimal physical information neural network model, which outputs the earth pressure prediction results.

[0016] An electronic device includes a processor, a memory, and a bus, wherein the processor and the memory are connected via the bus, wherein the memory is used to store a set of program code, and the processor is used to call the program code stored in the memory to execute a data- and physical dual-driven method for predicting earth pressure on a load-bearing shoulder retaining wall.

[0017] A non-volatile computer storage medium storing computer-executable instructions that execute a data- and physical dual-driven method for predicting earth pressure on a weighted shoulder retaining wall.

[0018] Compared with existing technologies, the present invention has the following advantages: (1) This invention adopts a dual-drive approach of data and physics, which deeply integrates the high-quality numerical data generated by adaptive finite element limit analysis with explicit differentiable physical laws to construct a physical information neural network, which significantly improves the prediction accuracy and generalization ability of earth pressure on counterweight shoulder retaining walls. Even in areas with sparse data, it can maintain the consistency between the prediction results and the basic laws of soil mechanics. It can simultaneously output key parameters in multiple dimensions such as earth pressure on the upper wall, lower wall, counterweight platform, and inclination angle of the rupture surface, providing a comprehensive and reliable mechanical basis for the refined design of retaining walls.

[0019] (2) This invention automatically generates a structured dataset covering multiple working conditions by combining Latin hypercube sampling with adaptive finite element limit analysis, which effectively reduces the dependence on scarce and costly measured data, solves the problem of poor model generalization ability caused by insufficient data in the field of geotechnical engineering by traditional data-driven methods, and greatly improves the engineering applicability and data utilization efficiency of the method.

[0020] (3) This invention realizes full-process automation from data generation and model training to earth pressure prediction, supports batch training of multiple models and automatic selection of the optimal model, and has a short prediction time for single working conditions, which significantly improves the calculation efficiency, reduces the workload of manual adjustment and repeated modeling, and can quickly respond to the needs of multi-scheme comparison and real-time prediction in engineering design. Attached Figure Description

[0021] Figure 1 This is an overall flowchart of the method of the present invention; Figure 2 This is a schematic diagram of the AFELA model and structure of the counterweight shoulder wall of the present invention; Figure 3 This is a schematic diagram of the Physical Information Neural Network (PINN) model architecture of the present invention; Figure 4 This is a flowchart of the model training process of the present invention; Figure 5 This is a comparison chart of the predicted and actual values ​​of the back earth pressure on the wall according to the present invention. Figure 6 This is a comparison chart of the predicted and actual values ​​of the soil pressure behind the wall according to the present invention. Figure 7 This is a comparison chart of the predicted and actual values ​​of the earth pressure on the weighing platform of this invention. Detailed Implementation

[0022] like Figure 1 As shown, the present invention provides a technical solution: a data- and physical dual-driven method for predicting earth pressure on a weighted shoulder retaining wall, comprising the following steps: Step S1: Construct an adaptive finite element limit analysis (AFELA) benchmark model, run the analysis to obtain the distribution of earth pressure on the back of the counterweight shoulder retaining wall and the morphology of the fracture surface under different working conditions, and provide a numerical benchmark for subsequent data generation and physical law extraction.

[0023] Step S2: Based on the benchmark model's running results and combined with earth pressure theory, extract the input parameters of the counterweight shoulder retaining wall structure and backfill material. Relying on Coulomb's earth pressure theory and the mechanism of the second rupture surface on the counterweight retaining wall, transform the physical laws of earth pressure calculation into differentiable mathematical constraints.

[0024] Step S3: Based on the input parameters of the benchmark model, the counterweight shoulder retaining wall structure and the backfill material, determine the range of input parameter values ​​according to the specifications, generate several sets of multi-condition parameters using Latin hypercube sampling, extract the target output parameters through automated modeling and calculation, and construct a structured dataset.

[0025] Step S4: Construct a data preprocessing module to periodically preprocess the operating parameters in the structured dataset.

[0026] Step S5: Establish a Physical Information Neural Network (PINN) model, design the network architecture, define a loss function that incorporates differentiable mathematical constraints, and use the Optuna hyperparameter optimization framework for automated tuning.

[0027] Step S6: Based on the optimized physical information neural network model and the structured dataset preprocessed by the data preprocessing module, perform batch model training and select the optimal physical information neural network model.

[0028] Step S7: Conduct earth pressure prediction, collect real-time input parameters of the counterweight shoulder retaining wall structure and backfill material, preprocess them through the data preprocessing module and input them into the optimal physical information neural network model, and output the earth pressure prediction results.

[0029] The specific process of step S1 is as follows: Step S11: First, based on the design drawings of the counterweight shoulder retaining wall, use Optum G2 software to establish a two-dimensional adaptive finite element limit analysis model, such as... Figure 2 As shown; Step S12: Set the material constitutive model, boundary conditions, and multiplier load conditions to simulate the actual working conditions; Step S13: Adaptive meshing technology is used to refine the mesh in stress concentration areas such as the contact area between the back of the counterweight shoulder retaining wall and the soil, and the potential rupture surface, to ensure the accuracy of earth pressure calculation. Step S14: Run adaptive finite element limit analysis to obtain the earth pressure distribution and rupture surface morphology of the counterweight shoulder retaining wall. Step S15: Verify the rationality of the two-dimensional adaptive finite element limit analysis model by comparing it with the earth pressure calculation method in the standard and the results in the literature, ensuring that the relative error is around 5% and that the simulation results conform to physical laws, so as to provide an accurate numerical analysis benchmark for subsequent earth pressure calculation.

[0030] The specific process of step S2 is as follows: Step S21: Analyze the dimensional sensitivity of the counterweight shoulder retaining wall structure and determine the total wall height of the counterweight shoulder retaining wall. The back slope angle of the upper wall of the counterweight shoulder retaining wall The back slope angle of the lower wall of a counterweight retaining wall Width of the weighing platform The structural input parameters can be selected as follows: the ratio of the upper and lower walls can be 4:6. Step S22: Analyze the fill material and determine the cohesion of the fill. The internal friction angle of the backfill Input parameters for the fill material; the present invention can also select the unit weight of the fill material. Input parameters for the fill material; Step S23: Based on Coulomb's earth pressure theory and the mechanism of the second rupture surface of a weighted retaining wall, establish a physical model for calculating earth pressure and extract the earth pressure function. Regarding the inclination angle of the second fracture surface on the wall Inclination angle of the first fracture surface on the wall The extreme value conditions (physical laws of earth pressure calculation) are satisfied and transformed into differentiable constraint conditions (providing a differentiable mathematical basis for embedding physical law constraints into the subsequent PINN model); the existing standard uses the calculation method of the second rupture surface of the upper wall, assuming that there are two rupture surfaces of the upper wall, but actual experiments and numerical simulations have verified that the first rupture surface of the upper wall was not generated. Step S24: Define the inclination angle of the second fracture surface on the upper wall. Inclination angle of the first fracture surface on the wall Boundary constraints: , .

[0031] In step S23, the earth pressure function Regarding the inclination angle of the second fracture surface on the wall Inclination angle of the first fracture surface on the wall The extreme value condition that is satisfied is expressed as: ; .

[0032] Among them, the earth pressure calculation formula (earth pressure function) ) is represented as: ; ; ; In the formula, This indicates the self-weight of the fractured wedge (referring to the weight per unit length of the wedge within the wall area, bounded by the first and second fracture surfaces and the back of the wall). Indicates the height of the wall; This represents the resultant earth pressure on the second rupture surface of the upper wall.

[0033] The specific process of step S3 is as follows: Step S31: Determine the input parameter range for the counterweight shoulder retaining wall structure and backfill material (based on the 5th edition of the Engineering Geology Handbook and relevant specifications): Wall height Back slope angle (1:0.25~1:0.45), Lower wall back slope angle (Default 1:0.25), Weighing platform width The internal friction angle of the backfill Cohesion of fill soil Based on the common soil classification in geotechnical engineering, the fill soil was divided into three categories: sand, silt, and clay. Latin hypercube sampling (LHS) was used to generate 360 ​​sets of working parameters (120 sets of working parameters were generated separately for each type of fill soil). A uniform random seed was used during sampling to ensure cohesion. With internal friction angle The positive correlation should be avoided to prevent parameter combinations that do not conform to the mechanical properties of soil. Step S32: Based on each set of working condition parameters, the automated modeling and calculation process is executed by calling automated modeling software in conjunction with the Adaptive Finite Element Limit Analysis (AFELA) benchmark model. Specifically: Based on each set of working condition parameters, an automated script is written in MATLAB (numerical calculation and programming software) to call OptumG2 (finite element professional modeling and calculation software) to perform batch parameter adaptation and automated modeling on the Adaptive Finite Element Limit Analysis (AFELA) benchmark model, generating executable calculation models corresponding to each working condition parameter; then, the calculation software is called in batches to perform limit analysis calculations, and the original results of the earth pressure on the wall back of each working condition are generated simultaneously; subsequently, the earth pressure data of all working conditions are automatically read, and the tangential and normal components of the earth pressure corresponding to the lower wall, upper wall, and counterweight are extracted according to coordinate partitions. The resultant force value of the earth pressure at each part under each working condition is obtained in batches through integration calculation, completing the fully automated batch modeling and calculation analysis process.

[0034] Step S33: Extract the back earth pressure of the counterweight shoulder retaining wall from the calculation results of each set of working parameters in step S32. Earth pressure behind the wall Earth pressure of the counterweight platform Inclination angle of the second fracture surface on the upper wall and the inclination angle of the first fracture surface on the wall As the target output parameter (label), a structured dataset containing the operating condition parameters and the corresponding target output parameters is constructed. Finally, the structured dataset is divided into training set, validation set and test set according to the ratio of 80% / 10% / 10%, and standardized (mean is 0, variance is 1, to eliminate the influence of the difference in units on the subsequent training of the Physical Information Neural Network (PINN) model), so as to provide high-quality structured data for subsequent model training.

[0035] Compared to simple random sampling, Latin hypercube sampling (LHS) can achieve uniform full coverage of the parameter space and avoid the problem of distribution bias. Latin hypercube sampling (LHS) can be mathematically described as follows: ; In the formula, Represents the sampling parameter matrix; Indicates wall height The sampled column vector; Indicates the width-to-height ratio of the weighing platform The sampled column vector; Indicates the back slope angle of the wall The sampled column vector; Indicates cohesion The sampled column vector; Indicates the internal friction angle The sampled column vector; * represents 5 input parameters ( , , , , ), ) is the first The corresponding parameter values ​​for the group of samples; The total number of samples is 120 groups each of sand, silt, and clay.

[0036] The specific process of step S4 is as follows: The data preprocessing module processes the wall back tilt angle in the working condition parameters of the structured dataset. Lower wall back slope angle Calculate the sin and cos values ​​respectively to form an 8-dimensional feature vector. ; sin / cos The transformation is used to handle periodic features (for the upper wall back tilt angle). , Lower wall back slope angle The sine and cosine values ​​are calculated separately to transform the periodic characteristics of the angle parameters into continuously differentiable numerical characteristics, which is used to improve the model's ability to fit angle changes and its generalization performance.

[0037] The specific process of step S5 is as follows: Step S51: Design the Physical Information Neural Network (PINN) model architecture: The input layer contains 8 nodes, corresponding to 8-dimensional feature vectors. ; The hidden layers contain multiple fully connected layers, using the Tanh activation function and batch normalization; The output layer contains 5 nodes, corresponding to the target output parameter: soil pressure on the wall. Earth pressure behind the wall Earth pressure of the counterweight platform Inclination angle of the second fracture surface on the upper wall and the inclination angle of the first fracture surface on the wall .

[0038] Step S52: Define the total loss function for the Physical Information Neural Network (PINN) model. The total loss function is obtained by weighted summation of the data loss term, the physical residual loss term, and the boundary constraint loss term. Each term corresponds to the data fitting weight, the physical constraint weight, and the boundary constraint weight, respectively, and is expressed as: ; In the formula, The weighting coefficients represent the data loss terms and are used to control the importance of the data fitting component in the total loss. Mean square error (MS) E Data loss; The weighting coefficient represents the physical residual loss term and is used to control the importance of physical constraints in the total loss. This represents the physical residual loss based on the differentiable constraint condition in step S23; The weighting coefficients of the boundary constraint loss term; For boundary constraint loss (for α , β (Impose penalties on the range of values). This invention Assign a value of 0, Fixed at 0.1, therefore This weighting term makes no actual contribution to the total loss calculation; Among them, mean square error data loss Used to measure the deviation between model predictions and measured label values, specifically for soil pressure on the wall. Earth pressure behind the wall Earth pressure of the counterweight platform The mean square error of these three types of target output parameters is calculated and expressed as follows: ; In the formula, This indicates the total number of samples participating in the calculation in the current batch; , , They represent the first The soil pressure on the wall of each sample Earth pressure behind the wall Earth pressure of the counterweight platform Predicted value; , , They represent the first i The soil pressure on the wall of each sample Earth pressure behind the wall Earth pressure of the counterweight platform Corresponding to the measured label value.

[0039] Among them, the physical residual loss of differentiable constraints The computational model outputs residuals that satisfy physical laws. Huber loss is used to improve numerical stability. The model is constrained by physical laws regarding the number of sampling points, PDE residuals, trainable parameters, partial derivatives of earth pressure, and threshold parameters. The partial derivatives of earth pressure are numerically solved using the finite difference method. The physical residual loss under differentiable constraints is also considered. Represented as: ; In the formula, This represents the number of sampling points constrained by physical laws, that is, the total number of points sampled in the parameter space during training to impose physical law constraints. Represents the Huber loss function; Represents the PDE residual term; Indicates the first The input parameters of the sampling points are constrained by physical laws. , , , , , ); The trainable parameters of a physical information neural network model; , The differential value of earth pressure is paired with , The partial derivatives, , The threshold parameter of the Huber loss function is solved numerically using the finite difference method. ; Among them, the Huber loss function Represented as: ; In the formula, The input variables for the Huber loss function; Among them, the PDE residual term Represented as: ; In the formula, Based on Coulomb's active earth pressure theory, by the first Geometric parameters of the retaining wall and soil mechanical parameters (wall height) corresponding to each sampling point internal friction angle Cohesion Reference angle of fracture surface Width of the weighing platform The theoretical value of earth pressure balance obtained by calculation (etc.) is used to characterize the standard physical quantity that satisfies the equilibrium condition of soil and rock mechanics.

[0040] Step S53: Using the Optuna hyperparameter optimization framework, with the goal of minimizing the PDE residuals on the validation set, a 20-round hyperparameter search of the physical information neural network model is carried out using TPESampler Bayesian sampling and MedianPruner pruning strategies (after a 20-step warm-up, the performance lag test is terminated). The optimization space includes: hidden layer dimension (128-320), number of network layers (4-8), learning rate (1e-5~5e-3), batch size (16 / 32 / 64 / 128), loss weights, and other hyperparameters. Step S54: Implement a dynamic loss weight scheduling strategy: Differentiately allocate loss weights according to the model training stage to achieve the training objective of "fitting data in the early stage, balancing constraints in the middle stage, and reinforcing physical laws in the later stage". The specific strategy is as follows: In the early stages of training (first 40% of rounds): focus on data fitting and set... , , ; Mid-training phase (40%-70% of rounds): Balancing data with physical constraints, setting... , , ; Later in the training phase (after 70% of the rounds): Strengthen the constraints of physical laws and set... , , .

[0041] The specific process of step S6 is as follows: Step S61: Based on the preprocessed structured dataset, build a standardized training framework for the physical information neural network model, clarify the core dependencies of the training environment (including core components such as deep learning framework, numerical computation library, and hyperparameter optimization library), and ensure the reproducibility of the training process. Step S62: Based on the optimized physical information neural network model and loss function, conduct multiple batch model training sessions, enabling an automatic hyperparameter optimization mechanism during training; such as... Figure 4 As shown, the preprocessed structured dataset is input into the model to start training. The training loss is continuously monitored. If the training loss does not converge, the training continues iteratively. If the training loss converges, the model output is further verified to meet the physical law constraints of earth pressure calculation. If not, the model is returned to retrain. Training is terminated after the model meets the constraints, so as to improve the model's generalization ability and fitting effect of physical law constraints. Step S63: After training is complete, construct a multi-dimensional comprehensive scoring system to quantitatively evaluate and rank all trained models. The scoring system mainly includes two types of indicators (each with a weight of 50%): 1. Model prediction accuracy metrics, based on , , average coefficient of determination Characterization; such as Figures 5-7 As shown in the figure (RMSE represents root mean square error), The predicted values ​​are closely distributed within the ±5% relative error line, and highly coincide with the 0% ideal fit line. The predicted values ​​are concentrated within ±5% relative error, indicating excellent fitting performance. The predicted values ​​have the highest degree of agreement with the benchmark values, and the error is strictly controlled within ±5%. 2. Model training stability metrics (weighted at 50%, comprehensively represented by the smoothness (variance) and convergence (final loss value) of the loss curve); Step S64: Based on the comprehensive scoring results, select the physical information neural network model with the best score as the final model for predicting earth pressure on the counterweight retaining wall. The comprehensive scoring formula for the physical information neural network model can be expressed as: ; In the formula, This represents the overall score of the physical information neural network model. This represents the model's prediction accuracy index; Indicates the stability index of model training; Step S55: Based on the score ranking or by viewing the results of each model, freely select the optimal model, automatically save the selection results, and package them into a dedicated prediction model package to provide the optimal model carrier for subsequent earth pressure prediction.

[0042] Step S7 involves multi-dimensional verification and evaluation of the prediction results, including verification of the satisfaction of physical law constraints (verifying the dip angle of the fracture surface). , The system performs quantitative assessment of prediction uncertainty and ultimately generates a visualized assessment report that includes dimensions such as the comparison between predicted and measured values ​​of earth pressure, prediction error distribution, and training and verification loss curves, thereby achieving accurate output of key parameters of earth pressure and rupture surface on the back of the counterweight shoulder retaining wall.

[0043] A second embodiment of the present invention also provides a data- and physical dual-driven system for predicting earth pressure on a weighted shoulder retaining wall, comprising: The Adaptive Finite Element Limit Analysis module is used to construct the Adaptive Finite Element Limit Analysis (AFELA) benchmark model, run the analysis to obtain the distribution of earth pressure on the back of the counterweight shoulder retaining wall and the morphology of the fracture surface under different working conditions, and provide a numerical benchmark for subsequent data generation and physical law extraction.

[0044] The physics knowledge extraction module is used to extract the input parameters of the counterweight shoulder retaining wall structure and backfill material based on the benchmark model running results and combined with earth pressure theory. Relying on Coulomb earth pressure theory and the second rupture surface mechanism of the counterweight retaining wall, the physical laws of earth pressure calculation are transformed into differentiable mathematical constraints.

[0045] The dataset construction module is used to determine the range of input parameter values ​​according to the specifications based on the input parameters of the benchmark model, the counterweight shoulder retaining wall structure and the backfill material, generate several sets of multi-condition parameters using Latin hypercube sampling, extract the target output parameters through automated modeling and calculation, and construct a structured dataset.

[0046] The parameter optimization module is used to build the data preprocessing module, which performs periodic preprocessing on the operating parameters in the structured dataset.

[0047] The model optimization module is used to build a Physical Information Neural Network (PINN) model, design the network architecture, define a loss function that incorporates differentiable mathematical constraints, and perform automated tuning using the Optuna hyperparameter optimization framework.

[0048] The model training module is used to perform batch model training and select the optimal physical information neural network model based on the optimized physical information neural network model and the structured dataset preprocessed by the data preprocessing module.

[0049] The real-time prediction module is used to predict earth pressure. It collects real-time input parameters of the counterweight shoulder retaining wall structure and backfill material. After preprocessing by the data preprocessing module, the data is input into the optimal physical information neural network model, which outputs the earth pressure prediction results.

[0050] A third embodiment of the present invention also provides an electronic device, including a processor, a memory, and a bus, wherein the processor and the memory are connected via the bus, wherein the memory is used to store a set of program code, and the processor is used to call the program code stored in the memory to execute a data and physical dual-drive method for predicting earth pressure on a load-bearing shoulder retaining wall.

[0051] A fourth embodiment of the present invention also provides a non-volatile computer storage medium storing computer-executable instructions that execute a data- and physical dual-driven method for predicting earth pressure on a weighted shoulder retaining wall.

[0052] To verify the superiority of the present invention, it was compared with the existing method on the same test set. The adaptive finite element limit analysis (AFELA) benchmark model data was used as the benchmark value. The detailed working conditions of the test set are shown in Table 1, the detailed results are shown in Table 2, and the error statistics are shown in Table 2. Table 1. Detailed parameters of test set 36 operating conditions Table 2. Error statistics of existing standard methods, the prediction method of this invention, and AFELA benchmark values ​​for the test set (36 operating conditions). As shown in Table 2, the prediction method of this invention is significantly superior to existing standard methods in terms of prediction accuracy, physical consistency, and comprehensiveness of engineering output. Moreover, the prediction efficiency meets the requirements of rapid engineering design and realizes full-process automation from data generation to model prediction, providing efficient and accurate earth pressure prediction support for the design of counterweight shoulder retaining walls.

[0053] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A data- and physical-driven method for predicting earth pressure on a weighted shoulder retaining wall, characterized in that, Includes the following steps: Step S1: Construct an adaptive finite element limit analysis benchmark model and run the analysis to obtain the distribution of earth pressure on the back of the counterweight shoulder retaining wall and the morphology of the rupture surface under different working conditions. Step S2: Based on the benchmark model running results and combined with earth pressure theory, extract the input parameters of the counterweight shoulder retaining wall structure and backfill material. Relying on Coulomb earth pressure theory and the mechanism of the second rupture surface of the counterweight retaining wall, transform the physical laws of earth pressure calculation into differentiable mathematical constraints. Step S3: Based on the input parameters of the benchmark model, the counterweight shoulder retaining wall structure and the backfill material, determine the range of input parameter values ​​according to the specifications, generate several sets of multi-condition parameters using Latin hypercube sampling, extract the target output parameters through automated modeling and calculation, and construct a structured dataset; Step S4: Construct a data preprocessing module to periodically preprocess the operating parameters in the structured dataset; Step S5: Establish a physical information neural network model, design the network architecture, define a loss function that incorporates differentiable mathematical constraints, and use the Optuna hyperparameter optimization framework for automated tuning; Step S6: Based on the optimized physical information neural network model and the structured dataset preprocessed by the data preprocessing module, perform batch model training and select the optimal physical information neural network model; Step S7: Conduct earth pressure prediction, collect real-time input parameters of the counterweight shoulder retaining wall structure and backfill material, preprocess the data through the data preprocessing module and input them into the optimal physical information neural network model to output the earth pressure prediction results.

2. The method for predicting earth pressure on a weighted shoulder retaining wall driven by both data and physical factors, as described in claim 1, is characterized in that: The specific process of step S1 is as follows: Based on the design drawings of the counterweight shoulder retaining wall, establish a two-dimensional adaptive finite element limit analysis model; set the material constitutive model, boundary conditions, and multiplier load conditions to simulate the actual working state; use adaptive mesh technology to refine the mesh in the stress concentration area of ​​the counterweight shoulder retaining wall; run the adaptive finite element limit analysis to obtain the earth pressure distribution and rupture surface morphology of the counterweight shoulder retaining wall; and compare and verify the rationality of the two-dimensional adaptive finite element limit analysis model.

3. The method for predicting earth pressure on a weighted shoulder retaining wall driven by both data and physical factors, as described in claim 2, is characterized in that: The specific process of step S2 is as follows: Analyze the dimensional sensitivity of the counterweight shoulder retaining wall structure and determine the total wall height of the counterweight shoulder retaining wall. The back slope angle of the upper wall of the counterweight shoulder retaining wall The back slope angle of the lower wall of a counterweight retaining wall Width of the weighing platform Input parameters for the structure; analyze the fill material and determine the cohesion of the fill. The internal friction angle of the backfill Input parameters for the backfill material; based on Coulomb's earth pressure theory and the mechanism of the second rupture surface of a weighted retaining wall, establish a physical model for earth pressure calculation and extract the earth pressure function. Regarding the inclination angle of the second fracture surface on the wall Inclination angle of the first fracture surface on the wall The extreme value conditions are satisfied and transformed into differentiable constraints; Define the inclination angle of the second fracture surface on the upper wall. Inclination angle of the first fracture surface on the wall Boundary constraints.

4. The method for predicting earth pressure on a weighted shoulder retaining wall driven by both data and physical factors, as described in claim 3, is characterized in that: The specific process of step S3 is as follows: determine the range of input parameter values ​​for the counterweight shoulder retaining wall structure and the backfill material; divide the backfill soil into three categories: sand, silt, and clay; based on the backfill soil type and the input parameters of the counterweight shoulder retaining wall structure and the backfill material, use Latin hypercube sampling to generate several sets of working condition parameters. Based on each set of working condition parameters, an automated modeling and calculation process is executed by calling automated modeling software in conjunction with an adaptive finite element limit analysis benchmark model. Extract the back earth pressure of the counterweight shoulder retaining wall from the calculation results of each set of working conditions. , soil pressure behind the wall Earth pressure of the weighing platform Inclination angle of the second fracture surface on the upper wall and the inclination angle of the first fracture surface on the wall As the target output parameter, construct a structured dataset containing operating condition parameters and corresponding target output parameters.

5. The method for predicting earth pressure on a weighted shoulder retaining wall driven by both data and physical factors, as described in claim 4, is characterized in that: The specific process of step S4 is as follows: The data preprocessing module processes the wall back tilt angle in the working condition parameters of the structured dataset. Lower wall back slope angle Calculate the sin and cos values ​​respectively to form an 8-dimensional feature vector. .

6. The method for predicting earth pressure on a weighted shoulder retaining wall driven by both data and physical factors, as described in claim 5, is characterized in that: The specific process of step S5 is as follows: Design a neural network model architecture for physical information: The input layer contains 8 nodes, corresponding to 8-dimensional feature vectors. ; The hidden layers contain multiple fully connected layers, using the Tanh activation function and batch normalization; The output layer contains 5 nodes, corresponding to the target output parameter: soil pressure on the wall. , soil pressure behind the wall Earth pressure of the weighing platform Inclination angle of the second fracture surface on the upper wall and the inclination angle of the first fracture surface on the wall ; The total loss function of the physical information neural network model is defined. This total loss function is obtained by a weighted sum of the data loss term, the physical residual loss term, and the boundary constraint loss term. Each term corresponds to the data fitting weight, the physical constraint weight, and the boundary constraint weight, respectively. The data loss term measures the deviation between the predicted values ​​of the physical information neural network model and the measured label values. The physical residual loss term is calculated using Huber loss, based on the number of sampling points constrained by physical laws, the PDE residual term, the trainable parameters of the model, the partial derivatives of earth pressure, and the threshold parameters. The partial derivatives of earth pressure are numerically solved using the finite difference method. Using the Optuna hyperparameter optimization framework, with the goal of minimizing PDE residuals, and employing Bayesian sampling and pruning strategies, we conducted hyperparameter search for the physical information neural network model. Loss weights are allocated differently based on the training stage of the physical information neural network model.

7. The method for predicting earth pressure on a weighted shoulder retaining wall driven by both data and physical factors, as described in claim 6, is characterized in that: The specific process of step S6 is as follows: Based on the preprocessed structured dataset, a standardized physical information neural network model training framework is built; based on the optimized physical information neural network model and loss function, multiple batch model trainings are carried out; after training, a multi-dimensional comprehensive scoring system is constructed to quantitatively evaluate and rank all trained models; based on the comprehensive scoring results, the physical information neural network model with the best score is selected.

8. A data- and physical-driven earth pressure prediction system for a weighted shoulder retaining wall, characterized in that, include: The adaptive finite element limit analysis module is used to construct an adaptive finite element limit analysis benchmark model and run the analysis to obtain the distribution of earth pressure on the back of the counterweight shoulder retaining wall and the morphology of the rupture surface under different working conditions. The physical knowledge extraction module is used to extract the input parameters of the counterweight shoulder retaining wall structure and backfill material based on the benchmark model running results and combined with earth pressure theory. Relying on Coulomb earth pressure theory and the mechanism of the second rupture surface of the counterweight retaining wall, the physical laws of earth pressure calculation are transformed into differentiable mathematical constraints. The dataset construction module is used to determine the range of input parameter values ​​according to the specifications based on the input parameters of the benchmark model, the counterweight shoulder retaining wall structure and the backfill material, generate several sets of multi-condition parameters using Latin hypercube sampling, extract the target output parameters through automated modeling and calculation, and construct a structured dataset. The parameter optimization module is used to build the data preprocessing module, which performs periodic preprocessing on the operating parameters in the structured dataset. The model optimization module is used to build a physical information neural network model, design the network architecture, define a loss function that incorporates differentiable mathematical constraints, and use the Optuna hyperparameter optimization framework for automated tuning. The model training module is used to perform batch model training and select the optimal physical information neural network model based on the optimized physical information neural network model and the structured dataset preprocessed by the data preprocessing module. The real-time prediction module is used to predict earth pressure. It collects real-time input parameters of the counterweight shoulder retaining wall structure and backfill material. After preprocessing by the data preprocessing module, the data is input into the optimal physical information neural network model, which outputs the earth pressure prediction results.

9. An electronic device, characterized in that, The system includes a processor, a memory, and a bus, wherein the processor and the memory are connected via the bus, the memory is used to store a set of program codes, and the processor is used to call the program codes stored in the memory to execute a data and physical dual-drive method for predicting earth pressure on a weighted shoulder retaining wall as described in any one of claims 1-7.

10. A non-volatile computer storage medium storing computer-executable instructions, characterized in that, The computer can execute instructions to perform the data- and physical dual-driven method for predicting earth pressure on a weighted shoulder retaining wall as described in any one of claims 1-7.

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