Frost-susceptible subgrade thaw settlement prediction method driven by multi-source data and deep learning

Abstract

The present application provides a method for predicting thaw settlement of frozen soil subgrade driven by multi-source data and deep learning, which relates to the field of cold region engineering. The method includes: obtaining a thermal-mechanical coupling physical model of the frozen soil subgrade by mathematically describing the thermal-mechanical coupling process of the frozen soil subgrade; collecting on-site monitoring data, remote sensing data, indoor test data and engineering environment data of the frozen soil subgrade, and obtaining a multi-source data set for constructing and training a physics-informed neural network model through cleaning and normalizing the multi-source data; constructing a physics-informed neural network based on the physical model of the frozen soil subgrade and the multi-source data set; constructing a physical residual of the physics-informed neural network model through a differential equation, and constructing a loss function based on the residual term; training the physics-informed neural network model to obtain a deep learning model for predicting the thaw settlement deformation of the frozen soil subgrade. This method can improve the accuracy and reliability of predicting the thaw settlement deformation of the frozen soil subgrade.

Description

Technical Field

[0001] This application relates to the technical field of cold region engineering, and specifically relates to a method for predicting the thaw settlement of frozen soil subgrade driven by multi-source data and deep learning. Background Technique

[0002] Due to the existence of underlying permafrost in the road engineering in permafrost regions, the occurrence of diseases therein involves complex multi-physical field coupling effects. With the global climate warming and the intensification of human activities, permafrost highways show a trend that the disease development process is difficult to accurately predict and the disease degree changes suddenly, which brings severe challenges to the efficient and intelligent operation and maintenance of road engineering.

[0003] Traditional evaluation methods mainly rely on finite element or finite difference numerical simulations and on-site monitoring means of single data sources. Due to the complex non-linear coupling effect between the internal temperature field and stress field of frozen soil and key physical phenomena such as the release of latent heat during the phase change process, traditional numerical models often need to simplify the control equations, resulting in the prediction results being difficult to accurately describe the disease degree of roads under complex environmental effects. In addition, key parameters involved in the model such as latent heat of phase change, critical stress, and reference temperature usually rely on prior experimental data or literature data preset, lacking the ability of on-site adaptive adjustment; and the data collected by a single monitoring method are also difficult to comprehensively reflect the complex distribution characteristics of the internal temperature and stress fields of the subgrade in terms of spatial and temporal resolution and coverage, thus limiting the real-time monitoring and accurate prediction of the disease evolution trend.

[0004] To solve the above problems, there is an urgent need to develop a method that can achieve real-time and accurate prediction of the thaw settlement disease of permafrost subgrade. This application constructs a Physics-Informed Neural Network (PINN), embeds physical control equations in the network loss function, and uses automatic differentiation technology to accurately solve the key partial derivatives, realizing the organic combination of data-driven and physical constraints, so as to be able to predict the thermo-mechanical coupling behavior and disease evolution trend of frozen soil subgrade with high precision and in real time. This provides a scientific basis and decision-making support for the efficient and intelligent operation and maintenance of roads, and has important theoretical significance and broad engineering application prospects. Summary of the Invention

[0005] This application provides a method for predicting the thaw settlement of frozen soil subgrade driven by multi-source data and deep learning, which can improve the accuracy and reliability of predicting the thaw settlement deformation of frozen soil subgrade.

[0006] Mathematically model the thermo-mechanical coupling process of the frozen soil subgrade, and establish a thermo-mechanical coupling physical model of the frozen soil subgrade with displacement as the main unknown; the thermo-mechanical coupling physical model includes a heat conduction model and a mechanical model. Among them, the heat conduction model is used to describe the evolution of the temperature field and the influence of the latent heat effect on the effective specific heat capacity and thermal conductivity during the phase change process;

[0007] Collect multi-source data on the frozen soil subgrade site. Through cleaning and normalizing the multi-source data, obtain a multi-source data set for constructing and training the physics-informed neural network model; the multi-source data includes monitoring data, remote sensing data, indoor test data, and engineering environment data;

[0008] Construct a physics-informed neural network based on the thermo-mechanical coupling physical model of the frozen soil subgrade and the multi-source data set; among them, the input of the physics-informed neural network is spatial coordinates and time, and the output is predicted temperature, settlement, and learnable parameters. The physics-informed neural network calculates the partial derivatives of the output with respect to space, time, and learnable parameters through an automatic differentiation mechanism, and the partial derivatives are used to construct the residual term of the thermo-mechanical coupling physical model of the frozen soil subgrade;

[0009] Construct a physical residual of the physics-informed neural network model through a differential equation, and construct a loss function based on the residual term; among them, the loss function is used to guide the training process of the physics-informed neural network to ensure that the model prediction results conform to the laws of classical physical models;

[0010] Train the physics-informed neural network to obtain a deep learning model when the loss function converges or reaches a preset number of training epochs. The deep learning model is used to predict the thaw settlement deformation of the frozen soil subgrade.

[0011] In some embodiments, the mathematical physics models for constructing the loss function of the physics-informed neural network include:

[0012] Heat conduction equation:

[0013]

[0014]

[0015]

[0016] Among them, is the natural density of the soil; = represents the specific heat capacity of the soil; and are the specific heat capacities of melting and freezing respectively; t is time; z is the spatial coordinate of depth; T is temperature; is the phase change temperature; is the phase change temperature range; = , representing the thermal conductivity of the soil; and represent the thermal conductivities in the melting and freezing states respectively; L is the latent heat;

[0017] Mechanical equation:

[0018]

[0019] where e is the void ratio, varying with the spatial coordinate z and time t with depth; is a function of the void ratio and temperature; , is the effective stress; and are the unit weights of soil and water respectively; is a function related to permeability and compressibility, , characterizes the functional relationship between the permeability coefficient and the void ratio; , is the initial void ratio, is the compression index, is the initial effective stress;

[0020] Based on the one-dimensional large deformation melting consolidation theory, the mechanical equation is transformed into a displacement control equation directly describing the settlement;

[0021] Relationship between displacement gradient and void ratio:

[0022]

[0023] where, is the relationship between displacement gradient and void ratio, f is a function reflecting the non-linear relationship between void ratio and strain in the case of large deformation, determined by fitting experimental data; is the vertical displacement field, describing the settlement or swelling of the soil mass;

[0024] Control equation in displacement form:

[0025]

[0026] where, is the displacement of the soil mass;

[0027] Melting boundary equation:

[0028]

[0029] where, ​The parameters \(\beta\) and \(n\) are empirical parameters obtained by fitting experimental data or on-site measured data, or by adaptive inversion using a priori regularization terms during the training process, and are used to describe the movement law of the settlement surface over time.

[0030] In some embodiments, the high-order derivatives of the network output with respect to \(z\) and \(t\) are calculated using automatic differentiation techniques, and these derivatives are substituted into the heat conduction, displacement control, and melting boundary equations to construct physical residuals. The residual terms include:

[0031] Residual of the heat conduction equation: Established based on the heat conduction equation of the apparent heat capacity method;

[0032] Residual of the mechanical equation: Established based on the one-dimensional large deformation thaw consolidation theory;

[0033] Residual of the melting boundary equation: Established based on the melting boundary equation;

[0034] Residual of the data item: Used to compare the multi-source data of the frozen soil subgrade with the network output results;

[0035] Residual of the boundary condition: Used to ensure the satisfaction of the thermal and mechanical boundary conditions;

[0036] A priori regularization term for parameters: Constrains the missing parameters in the latent heat, critical stress, and the empirical parameters.

[0037] In some embodiments, the collection of the multi-source data of the frozen soil subgrade to obtain a multi-source data set for training the physics-informed neural network further includes:

[0038] Performing denoising operations, interpolation operations, and time and space unified alignment operations on the multi-source data, and comparing them in the same coordinate form with the output of the physics-informed neural network to form the measured data item of the loss function.

[0039] In some embodiments, during the training process, the key parameters in the physics-informed neural network are set as learnable constants, and the learning range of the key parameters is constrained by the a priori regularization term in the loss function ( ) 2 where the key parameters include, but are not limited to, the latent heat \(L\) and the critical stress \(\sigma_{c}\), \(\beta\), \(n\), \(\hat{\beta}\), \(\hat{n}\) are the parameter values predicted by the physics-informed neural network, and \(\beta_{0}\), \(n_{0}\) are the a priori values of the parameters. \(\hat{\beta}\), \(\hat{n}\), are the parameter values predicted by the physics-informed neural network, and \(\beta_{0}\), \(n_{0}\) are the a priori values of the parameters.

[0040] In some embodiments, the total loss function is constructed by weighted combination of the data fitting term, physical residual term, boundary condition residual term, and a priori regularization term. The total loss function is:

[0041]

[0042] Among them, is the data fitting term. is the number of observed data points for calculating the data fitting term; is at the spatial coordinate and time the predicted temperature value; is at the spatial coordinate and time the actual temperature value; is at the spatial coordinate and time the predicted settlement; is at the spatial coordinate and time the actual settlement.

[0043] is the heat conduction residual term; is the number of heat conduction residual points; is the residual term of the heat conduction equation;

[0044] is the mechanical residual term; is the number of mechanical residual points; is the residual term of the mechanical equation;

[0045] is the melting boundary residual term; is the number of melting boundary residual points; is the residual term of the melting boundary condition;

[0046] is the boundary condition residual term;

[0047] is the prior regularization term to restrict the key parameters latent heat L, melting boundary parameter β, n from deviating from the preset interval;

[0048] are the weight coefficients of each item, adjusted according to the actual situation to balance the influence of each part on the training.

[0049] In some embodiments, the physical information neural network is trained to obtain a frozen soil subgrade thaw settlement prediction model when the loss function converges or reaches the preset number of training rounds. The frozen soil subgrade thaw settlement prediction model is used to predict the thaw settlement deformation state of the frozen soil subgrade, including:

[0050] The physical information neural network is trained using a two-stage optimization strategy. In the first stage, the Adam optimizer is used for preliminary convergence at a first learning rate. In the second stage, a second-order optimization algorithm is used for fine convergence. When the loss function converges or reaches a preset number of training epochs, a deep learning model is obtained. The deep learning model is used to predict the thaw settlement deformation of frozen soil subgrades.

[0051] In some embodiments, during the training process, the heat transfer model and the soil settlement model are fused with measured multi-source data by calculating the equation residuals at selected spatio-temporal points and adding the observed data terms.

[0052] In some embodiments, the method further includes:

[0053] Define the unfrozen water content or the frozen water content additionally at the output end of the physical information neural network, and perform automatic differentiation on the time derivative of the unfrozen water content or the frozen water content to obtain the time derivative of the unfrozen water content or the frozen water content.

[0054] Introduce the time derivative into the heat transfer model, introduce the latent heat of phase change term, so that the phase change process is directly described during training, so that the residual terms of the temperature field, moisture field and stress field are included in the loss function, and the complete solution of multi-field coupling is realized.

[0055] In some embodiments, the method further includes:

[0056] Verify the accuracy of the prediction results of the deep learning model based on the comparison of finite difference, finite element numerical solutions or on-site data, and evaluate the reliability of the deep learning model.

[0057] Compared with the prior art, the beneficial effects of the present application are as follows: By embedding the thermo-mechanical coupling equation in the physical information neural network, the prediction results can be made more in line with physical laws. Through the multi-source data fusion technology, the survey data, on-site monitoring data, remote sensing images and laboratory test results are organically combined; and the model is continuously optimized during the deep learning training process, so that the model has higher robustness and adaptability to complex engineering scenarios, can significantly improve the fitting accuracy of the model to the actual working conditions, and reduce the risk of inaccuracy caused by insufficient single data or noise, thereby improving the accuracy of the model prediction results. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a schematic diagram of the steps of the wave height prediction method provided by the embodiment of the present application. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0059] The present application will be further described in detail below in conjunction with test examples and specific embodiments. However, it should not be understood that the scope of the above-mentioned subject matter of the present application is limited to the following embodiments. All technologies implemented based on the content of the present application fall within the scope of protection of the present application.

[0060] In the description of the specific embodiments of the present application, without special explanation, the expression terms indicating the orientation or positional relationship such as "upper", "lower", "left", "right", "center", "inner", "outer", "side", etc. are all based on the orientation or positional relationship shown in the drawings, or the orientation or positional relationship when the product / device / device is usually used and placed. These terms of orientation or positional relationship are only for the convenience of describing the solution of the present application or simplifying the description in the specific embodiments, so as to facilitate technicians to quickly understand the solution, rather than indicating or implying that a specific device / component / element must have a specific orientation, or be constructed and operated in a specific positional relationship. Therefore, it should not be construed as a limitation to the present application.

[0061] In the description of the embodiments of the present application, technical terms such as "first" and "second" only distinguish one entity or operation from another entity or operation, and cannot be understood as indicating or implying relative importance or implicitly indicating the quantity, specific order or primary and secondary relationship of the indicated technical features. In the description of the embodiments of the present application, the meaning of "a plurality" is two or more, unless otherwise specifically defined.

[0062] Referring to "embodiment" herein means that a specific feature, structure or characteristic described in connection with the embodiment may be included in at least one embodiment of the present application. The phrase appears in various places in the specification and does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment mutually exclusive with other embodiments. Those skilled in the art explicitly and implicitly understand that the embodiments described herein can be combined with other embodiments.

[0063] Embodiment 1

[0064] Please refer to Figure 1 , Figure 1 which is a schematic diagram of the steps of the permafrost subgrade thaw settlement prediction method driven by multi-source data and deep learning provided by the embodiments of the present application. The steps of the permafrost subgrade thaw settlement prediction method driven by multi-source data and deep learning may include:

[0065] S1. Mathematically model the thermo-mechanical coupling process of the permafrost subgrade, and establish a thermo-mechanical coupling physical model of the permafrost subgrade with displacement as the main unknown quantity.

[0066] Among them, the thermo-mechanical coupling physical model includes a heat conduction model and a mechanical model. The heat conduction model is used to describe the evolution of the temperature field and the influence of the latent heat effect on the effective specific heat capacity and thermal conductivity during the phase change process. In the thermo-mechanical coupling physical model, the displacement u(z,t) is the main unknown. The explicit heat capacity method is adopted in the heat conduction part to describe the evolution of the temperature field T(z,t), reflecting the melting process and latent heat effect caused by temperature rise; in the mechanical part, based on the one-dimensional large deformation melting and consolidation theory, the relationship between the void ratio and the displacement gradient is approximately transformed into a displacement control equation directly describing the settlement deformation, reflecting the settlement displacement of the frozen soil subgrade soil with temperature change.

[0067] S2. Collect multi-source data of the frozen soil subgrade site. Through cleaning and normalizing the multi-source data, a multi-source data set for constructing and training the physics-informed neural network model is obtained.

[0068] Among them, the multi-source data includes monitoring data, remote sensing data, indoor test data, and engineering environment data.

[0069] S3. Construct a physics-informed neural network based on the thermo-mechanical coupling physical model of the frozen soil subgrade and the multi-source data set.

[0070] Among them, the input of the physics-informed neural network is the spatial coordinate and time, and the output is the predicted temperature, settlement amount, and learnable parameters. The physics-informed neural network calculates the partial derivatives of the output with respect to the space, time, and learnable parameters through the automatic differentiation mechanism, and the partial derivatives are used to construct the residual terms of the heat transfer model and the soil settlement model.

[0071] S4. Construct the physical residual of the physics-informed neural network model through differential equations, and construct a loss function based on the residual terms.

[0072] Among them, the loss function is used to guide the training process of the physics-informed neural network to ensure that the model prediction results conform to the laws of classical physical models.

[0073] S5. Train the physics-informed neural network to obtain a deep learning model when the loss function converges or reaches the preset number of training rounds. The deep learning model is used to predict the thaw settlement deformation of the frozen soil subgrade.

[0074] There is ice in the frozen soil, which remains stable under low temperature conditions. However, when the temperature rises, the ice will melt, causing changes in the soil structure, and then leading to subgrade settlement, deformation, and even damage. The method provided in this application can be applied to the prediction of thaw settlement of frozen soil subgrades, and predict and evaluate the possible melting and settlement (subsidence) of frozen soil subgrades under temperature rise or external condition changes.

[0075] In the embodiments of the present application, a thermo-mechanical coupling physical model control equation set is established based on the one-dimensional large deformation melting consolidation theory, the heat conduction equation of the apparent heat capacity method, and the melting boundary equation. Combining the physics-informed neural network model and multi-source data-driven, a deep learning model with physical constraints is formed for predicting the settlement amount.

[0076] In step S1, during the selection of the physical model, in the one-dimensional scenario, the roadbed direction is z ∈ [0, H], z = 0 is the ground (road surface), and z = H is the lower boundary; ignoring the lateral variation and the influence of lateral water flow, the main concern is the temperature field T(z, t) and the settlement u(z, t) evolving with time t.

[0077] The mathematical physics model for constructing the loss function of the physics-informed neural network includes:

[0078] Heat conduction equation:

[0079]

[0080]

[0081]

[0082] Among them, is the natural density of the soil; = represents the specific heat capacity of the soil; and are the specific heat capacities of melting and freezing respectively; t is time; z is the spatial coordinate of depth; T is temperature; is the phase change temperature; is the phase change temperature range; = represents the thermal conductivity of the soil; and represent the thermal conductivities in the melting and freezing states respectively; L is the latent heat.

[0083] Mechanical equation:

[0084]

[0085] Among them, e is the void ratio, which varies with the spatial coordinate z of depth and time t; is a function of the void ratio and temperature; , is the effective stress; and are the unit weights of soil and water respectively; is a function related to permeability and compressibility, , characterizes the functional relationship between the permeability coefficient and the void ratio; , is the initial void ratio, is the compression index, is the initial effective stress;

[0086] Based on the one-dimensional large deformation melting consolidation theory, the mechanical equation is transformed into a displacement control equation that directly describes the settlement;

[0087] Relationship between displacement gradient and void ratio:

[0088]

[0089] where, is the relationship between displacement gradient and void ratio, f is a function that reflects the non-linear relationship between void ratio and strain under large deformation conditions, determined by fitting experimental data; is the vertical displacement field, describing the settlement or swelling of the soil mass;

[0090] Control equation in displacement form:

[0091]

[0092] where, is the displacement of the soil mass;

[0093] Melting boundary equation:

[0094]

[0095] where, and n are empirical parameters, obtained by fitting experimental data or field measured data, or through adaptive inversion with a priori regularization terms during the training process, and are used to describe the movement law of the settlement surface over time.

[0096] When constructing the physics-informed neural network, in order to ensure that the model prediction results conform to physical laws, in the embodiments of the present application, physical constraints are embedded into the loss function of the neural network. This can force the model to follow basic physical laws during the training process.

[0097] In the embodiments of the present application, a physics-informed neural network is constructed, and automatic differentiation and physical equation residuals are used to model the thermodynamic and mechanical behaviors of the frozen soil subgrade.

[0098] The neural network structure can be:

[0099] Input layer, the input variables are spatial coordinates z and time t , hidden layer: several layers, such as 46 layers, with 64 or 128 neurons in each layer, and the activation function can be selected as tanh or ReLU, used to introduce non-linearity; the output variable is the predicted temperature​T pred and displacement u pred , that is T pred , u pred .

[0100] In PyTorch, the automatic differentiation function is used to calculate the derivatives of the output variables T pred and u pred to construct the residuals of the physical equations, specifically including: the time derivative , the second-order spatial derivative , the convective term derivative , etc.

[0101] In the embodiments of the present application, the total loss function is constructed by weighted combination of the data fitting term, the physical residual term, the boundary condition residual, and the prior regularization term. The total loss function is:

[0102]

[0103] where is the data fitting term; is the number of observed data points for calculating the data fitting term; is the predicted temperature value at the spatial coordinate and time ; is the actual temperature value at the spatial coordinate and time ; is the predicted settlement amount at the spatial coordinate and time ; is the actual settlement amount at the spatial coordinate and time ;

[0104] is the heat conduction residual term; is the number of heat conduction residual points; is the residual term of the heat conduction equation;

[0105] is the mechanical residual term; is the number of mechanical residual points; is the residual term of the mechanical equation;

[0106] is the melting boundary residual term; is the number of melting boundary residual points; is the residual term of the melting boundary condition;

[0107] is the residual term of the boundary condition;

[0108] is the prior regularization term to restrict the latent heat L, melting boundary parameter β, and n of the key parameters from deviating from the preset interval;

[0109] are the weight coefficients of each term, which are adjusted according to the actual situation to balance the influence of each part on the training.

[0110] The physical residual is the deviation between the predicted value of the neural network and the physical equation, which is used to measure whether the model conforms to the physical law. In this application, the loss function of the physical information neural network includes the following residual terms:

[0111] Residual of the heat conduction equation: established according to the heat conduction equation of the apparent heat capacity method; Residual of the mechanical equation: established according to the one-dimensional large deformation melting consolidation theory; Residual of the melting boundary equation: established according to the melting boundary equation; Residual of the data term: used to compare the multi-source data of the frozen soil subgrade with the network output result; Residual of the boundary condition: used to ensure the satisfaction of the thermal and mechanical boundary conditions; Parameter prior regularization term: to constrain the missing parameters in the latent heat, critical stress, and empirical parameters.

[0112] Among them, the residual of the heat conduction equation and the residual of the mechanical equation are respectively:

[0113]

[0114]

[0115] By minimizing the physical residual, it is ensured that the prediction result of the neural network conforms to the physical law, and the residuals of the heat conduction equation and the mechanical equation are optimized simultaneously, realizing the coupled solution of the temperature field and the displacement field. Physical constraints are introduced on the basis of data-driven to improve the generalization ability and prediction accuracy of the model.

[0116] The loss function constructed in the embodiment of this application combines the observation error, physical equation residual, parameter prior, and boundary condition error, and controls the importance of each item through different weights, which can be used to guide the training to obtain a model that not only conforms to the physical law but also can accurately predict the thaw settlement deformation state of the frozen soil subgrade.

[0117] In step S2, the temperature observation data in the multi-source data may include the temperature changes at different depths of the frozen soil subgrade obtained by burying sensors, and the settlement observation data may be the settlement amounts at different positions and different times of the subgrade observed by a total station or a laser rangefinder. The laboratory geotechnical test data may include parameters such as the thermal conductivity, compression modulus, and ice content of the soil. The remote sensing data may include the surface temperature obtained by the Moderate Resolution Imaging Spectroradiometer (MODIS), Landsat, or unmanned aerial vehicle (UAV) infrared images, and the surface settlement distribution obtained by the Synthetic Aperture Radar (SAR) or UAV oblique photography. The construction of the multi-source dataset may be to unify the spatio-temporal scales of the multi-source data to form a training set containing the input (spatial coordinates, time) and output (temperature, settlement amount).

[0118] The multi-source data may also include engineering and environmental data, such as heat source terms, such as geothermal flux and heat input from construction activities. Mass source terms, such as external water supply / loss conditions such as rainfall and drainage pipes. The boundary temperature reference T0 and amplitude T α , which can be set by meteorological data or historical experience and is used for the time-varying boundary conditions of the surface temperature.

[0119] The design of the Physics-Informed Neural Network (PINN) is that in its network structure, the input layer is the spatial coordinates (x, y, z) and time (t). The output layer is the predicted temperature (T), settlement amount (S), and learnable parameters such as the thermal conductivity k and latent heat of phase change L. The physical constraints of the Physics-Informed Neural Network are embedded by calculating the partial derivatives of the output with respect to the input (x, t) through the Automatic Differentiation technique. Substitute the partial derivatives into the heat transfer equation and the soil settlement equation to generate the residual term.

[0120] In the design of the loss function, the total loss function consists of a data term, an equation residual term, a parameter prior term, and a boundary condition term.

[0121] In the process of training the model, minimize the loss function through an optimization algorithm (such as Adam), and at the same time update the network parameters and learnable physical parameters. After training is completed, input any spatio-temporal coordinates (x, t), and the frozen soil subgrade thaw settlement prediction model can predict the future temperature field distribution and settlement amount, and dynamically evaluate the risk of frozen soil thaw settlement deformation.

[0122] In the above implementation process, by embedding the thermal-mechanical coupling equation in the physical information neural network, the prediction results can be made more consistent with physical laws. Through the multi-source data fusion technology, the survey data, on-site monitoring data, remote sensing images, and laboratory test results are organically combined; and the model is continuously optimized during the deep learning training process, enabling the model to have higher robustness and adaptability to complex engineering scenarios, which can significantly improve the fitting accuracy of the model to actual working conditions, reduce the risk of inaccuracy caused by insufficient single data or noise, and thus improve the accuracy of the model prediction results.

[0123] Embodiment 2

[0124] This embodiment is the implementation scheme for preprocessing multi-source data in the above Embodiment 1.

[0125] Preprocessing the multi-source data may include denoising operations, interpolation operations, and unified alignment operations in time and space for the multi-source data, and uniformly comparing them in the form of coordinates with the output of the physical information neural network to form the measured data item of the loss function.

[0126] Exemplarily, the denoising operation may include low-pass filtering and median filtering. The low-pass filtering can be based on smoothing the temperature and settlement data (eliminating high-frequency random interference). The formula example of discrete 1D low-pass filtering is:

[0127]

[0128] where is the value of the filtered signal at time point t represents the output result of low-pass filtering the original signal x ( t ); is the time point; N is the window length (number of points) of the filter, usually an odd number to ensure symmetry; is the normalization factor, which is used to convert the sum of the signals within the window into an average value to ensure that the amplitude of the output signal is consistent with the input signal.

[0129] For median filtering, when there are spike values in the settlement, the median method under the sliding window can be used to remove extreme anomalies.

[0130] The detection methods for outliers may include:

[0131] Z-score method: If , it is considered an outlier. Where is the value of the i-th data point, is the mean of the data set, k is the threshold coefficient, is the standard deviation of the data set.

[0132] IQR (Interquartile Range): If Values outside the range of Q1 - 1.5×IQR or Q3 + 1.5×IQR are considered abnormal.

[0133] The processing methods for outliers can include:

[0134] Interpolation method: linear / polynomial interpolation; Deletion: If the outlier is severe or an obvious error, the point can be deleted.

[0135] The methods for filling missing data can include:

[0136] For time series, linear interpolation and spline interpolation (such as for blank periods in x(t)) are used; for spatial data, methods such as Kriging and Inverse Distance Weighting (IDW) are used to fill in points.

[0137] The time and space alignment operations can include:

[0138] Unify the time step:

[0139] Interpolation: If the temperature sensor records once every 10 minutes and the settlement gauge records once a day, time interpolation / downsampling can be used to align them to the same time node (such as daily or hourly).

[0140] Downsampling: Average or filter high-frequency data to low-frequency; Upsampling: Interpolate low-frequency data to the high-frequency range.

[0141] Unify the spatial coordinate system:

[0142] Adopt a unified coordinate system (such as WGS84 or UTM), perform projection correction on remote sensing images, and ensure that the on-site monitoring points are consistent or matchable with the remote sensing pixels.

[0143] Grid matching: If the grid method is used, each grid corresponds to a position of (zi, ti) or (xi, yi, ti), and the data is interpolated into the grid.

[0144] In multi-source data, based on preprocessing, higher-level features can be extracted to enrich the model input. Higher-level features can include temperature features, settlement amount features, and laboratory parameters.

[0145] Temperature features can include the temperature gradient reflecting the heat conduction rate, the daily average temperature capturing the short-term average, and the seasonal or interannual cycles extracted through Fourier transform. Settlement amount features can include the settlement rate, cumulative settlement, and local settlement differences for comparing the spatial distribution of different monitoring points. Laboratory parameters can include the permeability coefficient k, thermal conductivity λ, specific heat capacity c, elastic modulus E, etc. Some of them are already constants in the target equation and can also be regarded as feature inputs.

[0146] Multi-source data can also be normalized and standardized, including linear normalization for scaling in the range of [0, 1] or [-1, 1] and zero-mean unit-variance normalization for deep learning models to stabilize the training process.

[0147] In the above implementation process, the denoising operation effectively removes the noise in the data, improves the reliability and quality of the data, reduces the interference of the noise on the model training, and thus enhances the generalization ability and prediction accuracy of the model. The interpolation operation can fill in the missing values in the data and improve the spatio-temporal continuity of the data, improve the integrity of the data, increase the density of data points, and enable the model to capture finer-grained physical phenomena. In addition, the unified alignment operation of time and space fuses the data from different sources into a unified coordinate system, eliminates the misalignment in time and space, improves the consistency between the data, and facilitates the accurate comparison with the output of PINN. Finally, by comparing the processed multi-source data with the output of PINN, the measured data item of the loss function is formed, enabling the loss function to more accurately reflect the deviation between the model output and the real data, and jointly guiding the model training in combination with the physical constraint term to ensure that the model conforms to both the measured data and the physical laws. Optionally, it can significantly improve the prediction accuracy, robustness, and engineering application value of the frozen soil subgrade thaw settlement prediction model, provide reliable technical support for the frozen soil subgrade thaw settlement prediction, and is applicable to dynamic monitoring and risk assessment in practical engineering.

[0148] Compared with the prior art, the present application can not only balance the rigor of the physical model and the fitting ability of deep learning, but also greatly improve the prediction accuracy and robustness through multi-source data fusion, and is more suitable for meeting the deformation prediction and disease prevention requirements of permafrost subgrade in a harsh environment.

[0149] Embodiment 3

[0150] This embodiment is a specific implementation scheme of the training process in Embodiment 1 above.

[0151] During the training process, the key parameters in the physics-informed neural network are set as learnable constants, and the learning range of the key parameters is constrained through the prior regularization term (param pred -param prior ) 2 in the loss function; among them, the key parameters include but are not limited to the latent heat L and the critical stress , param pred is the parameter value predicted by the physics-informed neural network, is the prior value of the parameter.

[0152] Among them, the prior regularization term (Prior Regularization) is used to constrain the learnable parameters (such as latent heat L, Critical stress σ A method (such as 0, etc.). By introducing the prior knowledge of parameters into the loss function, it is ensured that the parameters remain within a reasonable physical range during the learning process.

[0153] The form of the prior regularization term is usually:

[0154]

[0155] Where, is the parameter value predicted by the neural network (such as L , σ 0), is the prior value of the parameter, is the regularization coefficient, used to control the weight of the prior regularization term.

[0156] By introducing prior knowledge, the physical rationality of the parameter value can be improved, avoiding excessive deviation of the parameter from its physical meaning and preventing overfitting of the model. Combining the prior knowledge of the physical model with the data-driven method can improve the prediction accuracy and reliability of the model.

[0157] Key parameters such as latent heat L, critical stress σ0, reference temperature T r etc. usually need to be given in advance depending on literature or experiments. If the deviation is large, it will seriously affect the simulation results. In this application, by setting these unknown or difficult-to-measure parameters as learnable constants during the network training process, introducing the prior regularization term, and automatically inverting their optimal values using the measured data. It can automatically invert the key missing parameters, reduce the dependence on prior experience, and quickly adapt to complex engineering conditions. It can automatically identify the true properties of materials or environments, enabling the model to have greater adaptability under complex geological conditions and improving the prediction accuracy of the thaw settlement deformation of frozen soil subgrades.

[0158] During the training process, a two-stage optimization strategy can be adopted to train the physical information neural network. In the first stage, the Adam optimizer is used for preliminary convergence at the first learning rate, and in the second stage, a second-order optimization algorithm is used for fine convergence. To obtain a deep learning model when the loss function converges or reaches the preset number of training epochs, and the deep learning model is used to predict the thaw settlement deformation of the frozen soil subgrade.

[0159] Exemplarily, the training process may include:

[0160] Randomly initialize the network weights and σ pred 0, sample the data points (z i , t i ) to obtain , sample the physical points (z phys , t phys ) to calculate , by automatically differentiating in the forward + reverse directions and updating the weights, then repeating the iteration, first training for several rounds with the Adam optimizer and then using LBFGS for fine convergence, and outputting after convergence , , etc.

[0161] In addition, based on the thermo-mechanical coupling physical model, a moisture field can be added in the following way to construct a three-field coupling deep learning model:

[0162] Extraordinarily define the unfrozen water content or frozen water content at the output end of the physical information neural network, and automatically differentiate the time derivative of the unfrozen water content or the frozen water content to obtain the time derivative of the unfrozen water content or the frozen water content;

[0163] Introduce the time derivative into the heat conduction model, and directly describe the release or absorption of latent heat during the phase change process by introducing a latent heat term, so that in addition to the residual terms of the temperature field and the mechanical (settlement) field, the loss function also includes the residual term of the moisture field, so as to realize the three-field coupling solution of temperature, moisture and stress fields.

[0164] During the training process, multi-source data fusion of the heat conduction model, the mechanical model and the measured data can also be realized by calculating the equation residuals at selected spatio-temporal points and adding the observed data items.

[0165] When selecting spatial grids or spatio-temporal training points, adaptive sampling or regional sub-blocking techniques can be used to increase the sampling density in the regions containing phase change and convection, so as to accelerate convergence and improve the fitting accuracy of high-gradient regions, such as the phase change front.

[0166] Example 4

[0167] This embodiment of the present application is an embodiment for evaluating the prediction results of the frozen soil subgrade thaw settlement prediction model.

[0168] The method provided by this embodiment of the present application may further include:

[0169] Verify the accuracy of the prediction results of the deep learning model based on the comparison of finite difference, finite element numerical solutions or on-site data, and evaluate the reliability of the deep learning model.

[0170] In actual engineering applications, prototype verification can be first carried out in one-dimensional or small-scale two-dimensional scenarios, including comparing with finite difference / finite element numerical solutions to evaluate the temperature and settlement errors; after passing the verification, it can be extended to larger dimensions or complex creep conditions to meet the deformation prediction and safety assessment requirements of the full life cycle of roads in permafrost regions.

[0171] The above-described embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A frozen soil roadbed thawing settlement prediction method based on multi-source data and deep learning, characterized in that: include: Mathematical modeling is performed on the thermal-mechanical coupling process of the frozen soil roadbed, and a thermal-mechanical coupling physical model of the frozen soil roadbed with displacement as the main unknown quantity is established; wherein the thermal-mechanical coupling physical model includes a heat conduction model and a mechanical model, and the heat conduction model is used to describe the influence of the latent heat effect on the effective specific heat capacity and thermal conductivity during the evolution of the temperature field and the phase change process; Collect multi-source data from the frozen soil roadbed site, and obtain a multi-source data set for building and training a physical information neural network model by cleaning and normalizing the multi-source data; the multi-source data includes monitoring data, remote sensing data, indoor test data, and engineering environment data; A physical information neural network is constructed based on the thermal-mechanical coupling physical model of the frozen soil roadbed and the multi-source data set; wherein the input of the physical information neural network is spatial coordinates and time, and the output is predicted temperature, settlement and learnable parameters; the physical information neural network calculates the partial derivatives of the output with respect to space, time and learnable parameters through an automatic differentiation mechanism, and the partial derivatives are used to construct the residual term of the thermal-mechanical coupling physical model; The physical residual of the physical information neural network model is constructed by differential equations, and a loss function is constructed based on the residual term; wherein the loss function is used to guide the training process of the physical information neural network to ensure that the model prediction results conform to the laws of the classical physical model; The physical information neural network is trained to obtain a deep learning model when the loss function converges or reaches a preset number of training rounds; the deep learning model is used to predict the thawing settlement deformation of the frozen soil roadbed.

2. The method according to claim 1, characterized in that: The mathematical physics model for constructing the loss function of the physical information neural network includes: Heat conduction equation: in, is the natural density of the soil; = , represents the specific heat capacity of soil; and are melting and freezing specific heat capacities respectively; t is time; z is the spatial coordinate of depth; T is temperature; is the phase transition temperature; is the phase transition temperature range; = , represents the thermal conductivity of soil; and represent the thermal conductivity in the melting and freezing states respectively; L is the latent heat; Mechanical equations: Among them, e is the porosity ratio, which varies with the spatial coordinate z of the depth and time t; is a function of void ratio and temperature; , is the effective stress; and are the bulk densities of soil and water respectively; is a function related to permeability and compressibility, , Characterize the functional relationship between permeability coefficient and porosity ratio; , is the initial void ratio, is the compression index, is the initial effective stress; Based on the one-dimensional large deformation melting consolidation theory, the mechanical equation is transformed into a displacement control equation that directly describes the settlement; Relationship between displacement gradient and void ratio: ] in, is the relationship between displacement gradient and void ratio, f The function that reflects the nonlinear relationship between void ratio and strain under large deformation conditions is determined by fitting experimental data; is the vertical displacement field, describing the settlement or expansion of the soil; The governing equations in displacement form: in, is the displacement of the soil; Melt boundary equation: in, and n are empirical parameters, which are obtained by fitting experimental data or field measured data, or by adaptive inversion through prior regular terms during training, and are used to describe the movement law of the subsidence surface over time.

3. The method according to claim 2, characterized in that Automatic differentiation technology is used to calculate the high-order derivatives of the network output with respect to z and t, and these derivatives are substituted into the heat conduction, displacement control and melting boundary equations to construct the physical residual. The residual terms include: Heat conduction equation residual: heat conduction equation is established according to the apparent heat capacity method; Mechanical equation residual: established based on one-dimensional large deformation melting consolidation theory; Melt boundary equation residual: established according to the melt boundary equation; Data item residual: used to compare the multi-source data of the frozen soil roadbed with the network output results; Boundary condition residual: used to ensure that thermal and mechanical boundary conditions are met; Parameter prior regularization term: constrains the latent heat, critical stress, and missing parameters in the empirical parameters.

4. The method according to claim 1, characterized in that: The method of collecting multi-source data of frozen soil roadbed to obtain a multi-source data set for training a physical information neural network also includes: The multi-source data are subjected to denoising, interpolation and unified alignment in time and space, and are compared with the output of the physical information neural network in the form of coordinates to form measured data items of the loss function.

5. The method according to claim 1, characterized in that During the training process, the key parameters in the physical information neural network are set as learnable constants, and the prior regularization term in the loss function ( ) 2 Constrain the learning range of the key parameters; wherein the key parameters include but are not limited to latent heat L and critical stress ,β,n, is the parameter value predicted by the physical information neural network, is the prior value of the parameter.

6. The method according to claim 1, characterized in that By weighted combination of data fitting term, physical residual term, boundary condition residual term and prior regularization term, a total loss function is constructed, which is: in, is the data fitting term; The number of observed data points for calculating the data fitting term; In space coordinates and time The predicted temperature value at In space coordinates and time The actual temperature value; In space coordinates and time The predicted settlement at the In space coordinates and time The actual amount of settlement; is the heat conduction residual term; is the number of heat conduction residual points; is the residual term of the heat conduction equation; is the mechanical residual term; is the number of mechanical residual points; is the residual term of the mechanical equation; is the melting boundary residual term; is the number of melt boundary residual points; is the residual term of the melting boundary condition; is the residual term of boundary conditions; is a priori regularization term to limit the key parameters latent heat L, melting boundary parameter β, and n from deviating from the preset range; is the weight coefficient of each item, which is adjusted according to the actual situation to balance the impact of each part on training.

7. The method according to claim 1, characterized in that The physical information neural network is trained to obtain a deep learning model when the loss function converges or reaches a preset number of training rounds, and the deep learning model is used to predict the thawing deformation of the frozen soil roadbed, including: A two-stage optimization strategy is adopted to train the physical information neural network. In the first stage, the Adam optimizer is used to make preliminary convergence with a first learning rate, and in the second stage, a second-order optimization algorithm is used to make fine convergence. When the loss function converges or reaches a preset number of training rounds, a deep learning model is obtained. The deep learning model is used to predict the thaw settlement deformation of frozen soil roadbed.

8. The method according to claim 1, characterized in that: The method further comprises: During the training process, the equation residuals are calculated at selected time and space points and the observation data items are added to achieve multi-source data fusion of the heat conduction model, the mechanical model and actual measurements.

9. The method according to any one of claims 1 to 8, characterized in that: The method further comprises: On the basis of the thermal-mechanical coupling physical model, the moisture field is added in the following way to realize the construction of the three-field coupling deep learning model: An unfrozen water content or a frozen water content is additionally defined at the output end of the physical information neural network, and a time derivative of the unfrozen water content or the frozen water content is automatically differentiated to obtain the time derivative of the unfrozen water content or the frozen water content; The time derivative is introduced into the heat conduction model, and the release or absorption of latent heat in the phase change process is directly described by introducing the latent heat term, so that the loss function includes not only the residual terms of the temperature field and the mechanical field, but also the residual term of the moisture field, so as to realize the three-field coupling solution of the temperature, moisture and stress fields.

10. The method according to claim 1, characterized in that The method further comprises: The reliability of the deep learning model is evaluated by verifying the accuracy of the prediction results of the deep learning model based on comparison with finite differences, finite element numerical solutions or based on field data.

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