Frozen soil roadbed thaw collapse prediction method based on multi-source data and deep learning driving

Abstract

The invention provides a frozen soil roadbed thaw collapse prediction method based on multi-source data and deep learning driving, and relates to the field of cold region engineering. The method comprises the steps that mathematical description is conducted on the thermal-mechanical coupling process of the frozen soil roadbed, and a frozen soil roadbed thermal-mechanical coupling physical model is obtained; the method comprises the following steps: acquiring frozen soil roadbed field monitoring data, remote sensing data, indoor test data and engineering environment data, and performing cleaning and normalization processing on multi-source data to obtain a multi-source data set for constructing and training a physical information neural network model; constructing a physical information neural network based on the frozen soil roadbed physical model and the multi-source data set; constructing a physical residual error of the physical information neural network model through a differential equation, and constructing a loss function based on a residual error item; and training the physical information neural network model to obtain a deep learning model for predicting thaw collapse deformation of the frozen soil roadbed. According to the method, the accuracy and reliability of thaw collapse deformation prediction of the frozen soil roadbed can be improved.

Description

Technical Field

[0001] The present application relates to the field of cold region engineering technology, and in particular to a method for predicting thawing settlement of frozen soil roadbed based on multi-source data and deep learning. Background Art

[0002] Due to the existence of permafrost under the foundation, the generation of road diseases in permafrost areas contains complex multi-physical field coupling. With global warming and intensified human activities, permafrost roads show a trend of difficult to accurately predict the development of diseases and sudden changes in the degree of diseases, which brings severe challenges to the efficient and intelligent operation and maintenance of road projects.

[0003] Traditional assessment methods mainly rely on finite element or finite difference numerical simulation and on-site monitoring methods with a single data source. Due to the complex nonlinear coupling effect between the temperature field and stress field inside the frozen soil and key physical phenomena such as latent heat release during phase change, traditional numerical models often need to simplify the control equations, which makes it difficult for the prediction results to accurately describe the degree of road damage under the action of complex environments. In addition, key parameters such as phase change latent heat, critical stress and reference temperature involved in the model usually rely on prior experimental data or literature data presets, and lack on-site adaptive adjustment capabilities; and the data collected by a single monitoring method is also difficult to fully reflect the complex distribution characteristics of the temperature and stress field inside the roadbed in terms of temporal and spatial resolution and coverage, thereby limiting the real-time monitoring and accurate prediction of the evolution trend of the disease.

[0004] In order to solve the above problems, it is urgent to develop a method that can realize real-time and accurate prediction of thawing settlement of permafrost roadbed. This application constructs a physical information neural network (PINN), embeds physical control equations in the network loss function, and uses automatic differentiation technology to accurately solve key partial derivatives, so as to achieve an organic combination of data-driven and physical constraints, thereby enabling high-precision and real-time prediction of the thermal-mechanical coupling behavior and disease evolution trend of the frozen roadbed. This provides a scientific basis and decision-making support for efficient and intelligent operation and maintenance of roads, and has important theoretical significance and broad prospects for engineering applications. Summary of the invention

[0005] The present application provides a method for predicting the thawing settlement of frozen soil roadbed based on multi-source data and deep learning, which can improve the accuracy and reliability of thawing settlement deformation prediction of frozen soil roadbed.

[0006] 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; the thermal-mechanical coupling physical model includes a heat conduction model and a mechanical model, wherein 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 of the frozen soil roadbed; 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 deformation of the frozen soil roadbed.

[0007] In some embodiments, the mathematical physics model for constructing the loss function of the physical information neural network includes: Heat conduction equation:

[0008]

[0009]

[0010] 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:

[0011] 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 It is a function that reflects the nonlinear relationship between void ratio and strain under large deformation conditions and 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:

[0012] in, is the displacement of the soil; Melt boundary equation:

[0013] 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.

[0014] In some embodiments, automatic differentiation techniques are used to calculate 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 physical residuals, wherein 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 frozen soil roadbed with the network output result; 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.

[0015] In some embodiments, the collecting of multi-source data of the frozen soil roadbed to obtain a multi-source data set for training a physical information neural network further 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.

[0016] In some embodiments, during the training process, the key parameters in the physical information neural network are set as learnable constants, and the prior regularization term ( ) 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.

[0017] In some embodiments, a total loss function is constructed by weighted combination of data fitting terms, physical residual terms, boundary condition residual terms, and prior regularization terms. The total loss function is:

[0018] 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.

[0019] 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 boundary condition residual term; 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.

[0020] In some embodiments, the physical information neural network is trained to obtain a frozen soil roadbed thawing settlement prediction model when the loss function converges or reaches a preset number of training rounds, and the frozen soil roadbed thawing settlement prediction model is used to predict the thawing settlement deformation state 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.

[0021] In some embodiments, during the training process, the heat transfer model and the soil settlement model are fused with the measured multi-source data by calculating equation residuals at selected time and space points and adding observation data items.

[0022] In some embodiments, the method further comprises: 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 transfer model, and the phase change latent heat term is introduced, so that the phase change process can be directly described in the training, so that the residual terms of the temperature field, moisture field and stress field are included in the loss function, and a complete solution of multi-field coupling is achieved.

[0023] In some embodiments, 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.

[0024] Compared with the prior art, the beneficial effect of this application is that 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 multi-source data fusion technology, the survey data, field 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, which can significantly improve the model's fitting accuracy to actual working conditions, reduce the risk of inaccuracy caused by insufficient single data or noise, and thus improve the accuracy of the model's prediction results. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 A schematic diagram of the steps of the wave height prediction method provided in an embodiment of the present application. DETAILED DESCRIPTION

[0026] The present application is further described in detail below in conjunction with test examples and specific implementation methods. However, this should not be understood as the scope of the above subject matter of the present application being limited to the following embodiments, and all technologies implemented based on the content of the present application belong to the scope of protection of the present application.

[0027] Unless otherwise specified, in the description of the specific embodiments of the present application, the terms indicating the orientation or position relationship such as "up", "down", "left", "right", "center", "inside", "outside", "side", etc. are all expressions based on the orientation or position relationship shown in the drawings, or the orientation or position relationship when the product / equipment / device is usually used. These terms of orientation or position relationship are only for the convenience of describing the scheme of the present application or simplifying the description in the specific embodiments to facilitate the technicians to quickly understand the scheme, rather than indicating or implying that a specific device / component / element must have a specific orientation, or be constructed and operated in a specific position relationship, and therefore cannot be understood as a limitation on the present application.

[0028] In the description of the embodiments of the present application, the technical terms "first", "second", etc. 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 number, 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 "multiple" is two or more, unless otherwise clearly and specifically defined.

[0029] Reference to "embodiments" herein means that a particular feature, structure, or characteristic described in conjunction with the embodiments may be included in at least one embodiment of the present application. The appearance of the phrase in various locations in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment that is mutually exclusive with other embodiments. It is explicitly and implicitly understood by those skilled in the art that the embodiments described herein may be combined with other embodiments.

[0030] Example 1 Please see Figure 1 , Figure 1 A schematic diagram of the steps of a frozen soil roadbed thawing settlement prediction method based on multi-source data and deep learning driven provided in an embodiment of the present application. The steps of the frozen soil roadbed thawing settlement prediction method based on multi-source data and deep learning driven may include: S1. Mathematically model the thermal-mechanical coupling process of frozen soil roadbed and establish a physical model of thermal-mechanical coupling of frozen soil roadbed with displacement as the main unknown quantity.

[0031] Among them, the thermomechanical coupling physical model includes a heat conduction model and a mechanical model. 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. The displacement u(z,t) is the main unknown in the thermomechanical coupling physical model. The heat conduction part uses the apparent heat capacity method to describe the evolution of the temperature field T(z,t), reflecting the melting process and latent heat effect caused by the temperature increase; the mechanical part is based on the one-dimensional large deformation melting consolidation theory, and the relationship between the porosity and the displacement gradient is approximately converted into a displacement control equation that directly describes the settlement deformation, reflecting the settlement displacement of the frozen soil roadbed soil with temperature changes.

[0032] S2. 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.

[0033] The multi-source data include monitoring data, remote sensing data, indoor test data and engineering environment data.

[0034] S3. Constructing a physical information neural network based on the thermal-mechanical coupling physical model of the frozen soil roadbed and the multi-source data set.

[0035] Among them, 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. The partial derivatives are used to construct the residual terms of the heat transfer model and the soil settlement model.

[0036] S4. Construct the physical residual of the physical information neural network model through differential equations, and construct a loss function based on the residual term.

[0037] Among them, 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.

[0038] S5. Training the physical information neural network to obtain a deep learning model when the loss function converges or reaches a preset number of training rounds, wherein the deep learning model is used to predict the thawing deformation of the frozen soil roadbed.

[0039] Frozen soil contains ice, which remains stable under low temperature conditions, but when the temperature rises, the ice will melt, causing changes in the soil structure, which in turn causes roadbed settlement, deformation, and even damage. The method provided in this application can be applied to the prediction of thawing settlement of frozen soil roadbed, and predict and evaluate the melting and settlement (sinking) of frozen soil roadbed when the temperature rises or the external conditions change.

[0040] In an embodiment of the present application, a group of control equations of a thermomechanical coupling physical model 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. Combined with a physical information neural network model and multi-source data drive, a deep learning model with physical constraints is formed to predict the amount of settlement.

[0041] In step S1, during the selection of the physical model, the one-dimensional scene sets the roadbed direction z∈[0, H], z=0 as the ground (road surface), and z=H as the lower boundary; lateral changes and the influence of lateral water flow are ignored, and the main concern is the temperature field T(z, t) and settlement u(z, t) evolving with time t.

[0042] The mathematical physics model for constructing the loss function of the physical information neural network includes: Heat conduction equation:

[0043]

[0044]

[0045] 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 They represent the thermal conductivity in the melted and frozen states respectively; L is the latent heat.

[0046] Mechanical equations:

[0047] 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 It is a function that reflects the nonlinear relationship between void ratio and strain under large deformation conditions and 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:

[0048] in, is the displacement of the soil; Melt boundary equation:

[0049] 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.

[0050] When constructing a physical information 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 in the loss function of the neural network. This can force the model to follow basic physical laws during the training process.

[0051] In the embodiment of the present application, a physical information neural network is constructed, and automatic differentiation and physical equation residuals are used to achieve modeling of the thermodynamic and mechanical behaviors of the frozen soil roadbed.

[0052] The neural network structure can be: Input layer, input variables are spatial coordinates z and time t Hidden layers: several layers, such as 46 layers, with 64 or 128 neurons in each layer. The activation function can be tanh or ReLU to introduce nonlinearity; the output variable is the predicted temperature T pred and displacement u pred ,Right now[ T pred , u pred ].

[0053] In PyTorch, using automatic differentiation to calculate output variables T pred and u pred The derivatives of are used to construct the residuals of the physical equations, including: time derivatives , the spatial second-order derivative , the derivative of the convection term wait.

[0054] In the embodiment of the present application, a total loss function is constructed by weighted combination of data fitting terms, physical residual terms, boundary condition residual terms and prior regularization terms. The total loss function is:

[0055] 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 boundary condition residual term; 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.

[0056] The physical residual is the deviation between the neural network prediction value 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: Heat conduction equation residual: established according to the heat conduction equation of the apparent heat capacity method; mechanical equation residual: established according to the one-dimensional large deformation melting consolidation theory; melting boundary equation residual: established according to the melting 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 the satisfaction of thermal and mechanical boundary conditions; parameter prior regularization term: constrains the missing parameters in the latent heat, critical stress and the empirical parameters.

[0057] Among them, the residual of the heat conduction equation is and the residual of the mechanical equation They are:

[0058]

[0059] By minimizing the physical residuals, we ensure that the prediction results of the neural network conform to the physical laws, and the residuals of the heat conduction equation and the mechanical equation are optimized at the same time to achieve the coupled solution of the temperature field and the displacement field. On the basis of data-driven, physical constraints are introduced to improve the generalization ability and prediction accuracy of the model.

[0060] The loss function constructed in the embodiment of the present application integrates observation errors, physical equation residuals, parameter priors and boundary condition errors, and controls the importance of each item by different weights. It can be used to guide training to obtain a model that conforms to physical laws and can accurately predict the thawing deformation state of frozen soil roadbed.

[0061] In step S2, the temperature observation data in the multi-source data may include the temperature changes at different depths of the frozen soil roadbed obtained by burying sensors, and the settlement observation data may be the settlement of the roadbed at different positions and times observed by a total station or a laser rangefinder. Laboratory geotechnical test data may include parameters such as the thermal conductivity, compression modulus, and ice content of the soil. Remote sensing data may include surface temperature obtained by a Moderate Resolution Imaging Spectroradiometer (MODIS), Landsat or drone infrared imagery, and surface settlement distribution obtained by synthetic aperture radar (SAR) and drone oblique photography. The construction of a multi-source data set may be to unify the spatiotemporal scale of multi-source data to form a training set containing input (spatial coordinates, time) and output (temperature, settlement).

[0062] Multi-source data can also include engineering and environmental data, such as heat source items, such as geothermal flow, construction activity heat input. Mass source items, such as external water supply / loss from rainfall, drainage pipes, etc. 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.

[0063] The design of the physical information 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 (S) and learnable parameters, such as thermal conductivity k, phase change latent heat L, etc. The physical constraints of the physical information neural network are embedded in the automatic differentiation technology to calculate the partial derivatives of the output to the input (x, t). The partial derivatives are substituted into the heat transfer equation and the soil settlement equation to generate the residual term.

[0064] In the design of the loss function, the total loss function consists of data terms, equation residual terms, parameter prior terms, and boundary condition terms.

[0065] In the process of training the model, the loss function is minimized through optimization algorithms (such as Adam), and the network parameters and learnable physical parameters are updated at the same time. After the training is completed, any time and space coordinates (x, t) are input, and the frozen soil roadbed thaw settlement prediction model can predict the future temperature field distribution and settlement, and dynamically evaluate the risk of frozen soil thaw settlement deformation.

[0066] 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 multi-source data fusion technology, the survey data, field 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, which can significantly improve the model's fitting accuracy to actual working conditions and reduce the risk of inaccuracy caused by insufficient single data or noise, thereby improving the accuracy of the model's prediction results.

[0067] Example 2 This embodiment is an implementation plan for preprocessing multi-source data in the above embodiment 1.

[0068] Preprocessing of multi-source data may include denoising, interpolation, and unified alignment of time and space, and comparing the output of the physical information neural network in coordinate form to form measured data items of the loss function.

[0069] For example, the denoising operation may include low-pass filtering and median filtering. The low-pass filtering may be based on smoothing the temperature and sedimentation data (eliminating high-frequency random interference). An example of a discrete 1D low-pass formula is:

[0070] in, is the filtered signal at time point t The value of the original signal x ( t ) is the output result after low-pass filtering; is the time point; N is the filter window length (number of points), usually an odd number to ensure symmetry; is a normalization factor used to convert the accumulated sum of the signals in the window into an average value to ensure that the amplitude of the output signal is consistent with the input signal.

[0071] Median filtering can remove extreme anomalies by using the median method under a sliding window when a peak value appears in the sedimentation.

[0072] Methods for detecting outliers may include: Z-score method: If , it is considered abnormal. is the value of the ith data point, is the mean of the data set, k is the threshold coefficient, is the standard deviation of the data set.

[0073] IQR (interquartile range): If If it exceeds the range of Q1-1.5×IQR or Q3+1.5×IQR, it is considered abnormal.

[0074] Ways to handle outliers include: Interpolation method: linear / polynomial interpolation; Delete: If the abnormality is serious or obviously wrong, the point can be deleted.

[0075] Ways to fill in missing data can include: For time series, linear interpolation and spline interpolation (such as blank periods in x(t)) are used; for spatial data, Kriging, inverse distance weighted (IDW) and other methods are used to fill in points.

[0076] Temporal and spatial alignment operations can include: Uniform time step: Interpolation: If the temperature sensor records every 10 minutes and the sedimentation meter records once a day, time interpolation / downsampling can be used to align the two to the same time node (such as daily or hourly).

[0077] Downsampling: averaging or filtering high-frequency data to low frequency; upsampling: interpolating low-frequency data to high-frequency range.

[0078] Unified space coordinate system: Use a unified coordinate system (such as WGS84 or UTM) to perform projection correction on remote sensing images to ensure that the on-site monitoring points are consistent or matchable with the remote sensing pixels.

[0079] Grid matching: If the grid method is used, each grid corresponds to a (zi, ti) or (xi, yi, ti) position, and the data is interpolated to the grid.

[0080] In multi-source data, higher-level features can be extracted based on preprocessing to enrich model input. Higher-level features can include temperature features, sedimentation features, and laboratory parameters.

[0081] Temperature features can include temperature gradients reflecting the rate of heat transfer, daily average temperatures capturing short-term averages, and seasonal or interannual cycles extracted through Fourier transforms. Sedimentation features can include sedimentation rate, cumulative sedimentation, and local sedimentation differences comparing the spatial distribution of different monitoring points. Laboratory parameters can include permeability k, thermal conductivity λ, specific heat c, elastic modulus E, etc. Some of them are constants in the target equation and can also be regarded as feature inputs.

[0082] Multi-source data can also be normalized and standardized, including linear normalization for [0, 1] or [-1, 1] range scaling and zero-mean unit variance normalization for deep learning models to stabilize the training process.

[0083] 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 noise on model training, and thus enhances the generalization ability and prediction accuracy of the model. The interpolation operation can fill the missing values ​​in the data and improve the spatiotemporal continuity of the data, improve the integrity of the data, increase the density of data points, and enable the model to capture more fine-grained physical phenomena. In addition, the unified alignment operation of time and space integrates data from different sources into a unified coordinate system, eliminates the misalignment in time and space, improves the consistency between data, and facilitates accurate comparison with the output of PINN. Finally, by comparing the processed multi-source data with the output of PINN, the measured data term of the loss function is formed, so that the loss function can more accurately reflect the deviation between the model output and the real data, and jointly guide the model training in combination with the physical constraint term to ensure that the model is consistent with the measured data and follows the physical laws. The prediction accuracy, robustness and engineering application value of the frozen soil roadbed thaw settlement prediction model are significantly improved, providing reliable technical support for the prediction of frozen soil roadbed thaw settlement, which is suitable for dynamic monitoring and risk assessment in actual engineering.

[0084] Compared with the existing technology, this application not only takes into account the rigor of the physical model and the fitting ability of deep learning, but also greatly improves the accuracy and robustness of the prediction through multi-source data fusion, and is more suitable for meeting the deformation prediction and disease prevention and control needs of permafrost roadbed in harsh environments.

[0085] Example 3 This embodiment is a specific implementation plan of the training process in the above embodiment 1.

[0086] During the training process, the key parameters in the physical information neural network are set as learnable constants, and the prior regularization term (param pred -param prior ) 2 Constrain the learning range of key parameters; where key parameters include but are not limited to latent heat L and critical stress ,param pred is the parameter value predicted by the physical information neural network, is the prior value of the parameter.

[0087] Among them, the prior regularization term is used to constrain the learnable parameters in the neural network (such as latent heat L , critical stress σ 0, etc. By introducing prior knowledge of the parameters into the loss function, it ensures that the parameters remain within a reasonable physical range during the learning process.

[0088] The form of the prior regularization term is usually:

[0089] in, 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, which is used to control the weight of the prior regularization term.

[0090] By introducing prior knowledge, we can improve the physical rationality of parameter values, avoid excessive deviation of parameters from physical meaning, and prevent model overfitting. Combining prior knowledge of physical models with data-driven methods can improve the prediction accuracy and reliability of the model.

[0091] Latent heat L, critical stress σ0, reference temperature T r Key parameters such as , usually need to be given in advance through 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 network training, introducing a priori regularization terms, and automatically inverting their optimal values ​​using measured data. The key missing parameters can be automatically inverted, reducing dependence on prior experience and quickly adapting to complex engineering conditions. The real properties of materials or environments can be automatically identified, making the model more adaptive under complex geological conditions and improving the accuracy of prediction of thawing and settlement deformation of frozen soil roadbed.

[0092] During the training process, a two-stage optimization strategy can be used 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 thawing deformation of frozen soil roadbed.

[0093] For example, the training process may include: Randomly initialize network weights and σ pred 0, for data points (z i , t i ) Sampling acquisition , for the physical point (z phys , t phys ) Sampling calculation , calculated by automatic differentiation in the forward + backward direction And update the weights, then repeat the iteration, use the Adam optimizer to train for several rounds, then use LBFGS for fine convergence, and output after convergence , , wait.

[0094] In addition, based on the thermal-mechanical coupling physical model, the moisture field can be added in the following ways 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 (sedimentation) 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.

[0095] During the training process, the multi-source data fusion of the heat conduction model, the mechanical model and actual measurement can be realized by calculating the equation residuals at the selected time and space points and adding the observation data items.

[0096] When selecting spatial grids or spatiotemporal training points, adaptive sampling or regional blocking techniques can be used to increase the sampling density in regions containing phase change and convection to accelerate convergence and improve the fitting accuracy of high gradient regions such as phase change fronts.

[0097] Example 4 The embodiment of the present application is an embodiment of evaluating the prediction results of a frozen soil roadbed thaw settlement prediction model.

[0098] The method provided in the embodiment of the present application may also include: 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.

[0099] In actual engineering applications, prototype verification can first be carried out in one-dimensional or small-scale two-dimensional scenarios, including comparison with finite difference / finite element numerical solutions to evaluate temperature and settlement errors; once the verification is passed, it can be expanded to larger dimensions or complex creep conditions to meet the deformation prediction and safety assessment needs of roads in permafrost areas throughout their life cycle.

[0100] The embodiments described above 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 aforementioned embodiments, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions 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 It is a function that reflects the nonlinear relationship between void ratio and strain under large deformation conditions and 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 boundary condition residual term; 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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