Roadbed internal depth displacement prediction method fusing multi-physics field coupling mechanism and LSTM time sequence prediction model

Abstract

The invention discloses a roadbed internal depth displacement prediction method fusing a multi-physics field coupling mechanism and an LSTM time sequence prediction model. The method comprises the steps of obtaining initial conditions of a temperature field, a moisture field and a stress field in a to-be-predicted region; constructing a roadbed internal depth displacement prediction model, inputting the initial condition into the roadbed internal depth displacement prediction model for prediction, and obtaining a displacement prediction result; wherein the roadbed internal depth displacement prediction model is a physical constraint LSTM model and comprises a plurality of independent sub-networks, features of temperature, moisture and stress are extracted through the independent sub-networks, the features are fused, and a displacement prediction result is output. The method provides a theoretical basis and technical support for the disaster prediction of the loess low embankment in the seasonal frozen region, effectively reduces the roadbed disease repair cost, and guarantees the road service safety and economic sustainability.

Description

Technical Field

[0001] The present invention relates to the technical field of civil engineering health monitoring, and particularly to a method for predicting the internal depth displacement of a subgrade by integrating the coupling mechanism of multiple physical fields and an LSTM time series prediction model. Background Art

[0002] In the field of civil engineering, especially in the low embankment project of loess in seasonal frozen regions, the coupling effect of seasonal freeze-thaw and heavy traffic is the core cause of frequent subgrade diseases. In seasonal frozen regions such as Northeast and Northwest China, the average annual freeze-thaw cycle can reach 20 - 30 times. With the long-term action of heavy-duty vehicles (axle load ≥ 20 tons), the subgrade soil experiences repeated processes of frost heaving - thaw settlement - compaction, which further leads to catastrophic phenomena such as crack propagation and local collapse. According to statistics, the repair cost of highway subgrade diseases in seasonal frozen regions accounts for about 40% of the average annual maintenance funds, seriously threatening the service safety and economic sustainability of roads.

[0003] In the prior art, traditional numerical models such as the finite element method have obvious limitations in dealing with such problems. The finite element method is usually based on one-dimensional assumptions and steady-state simplifications, making it difficult to capture the long-term cumulative effects of freeze-thaw cycles and dynamic loads. For example, in simulating the freeze-thaw cycle process, the finite element method is difficult to accurately describe the nonlinear deformation and failure mechanism of soil under repeated freeze-thaw actions. In addition, when dealing with multi-field coupling problems, due to the complexity of physical equations, the training of the model is difficult, and it has a strong dependence on initial conditions and boundary conditions, resulting in certain limitations in practical engineering applications.

[0004] Although data-driven models such as deep learning are good at time series modeling, they also face many difficulties in dealing with catastrophic problems of multi-field coupling and time series nonlinearity. These models usually require a large amount of measured data for training and lack explicit constraints on physical laws, resulting in poor performance in generalization ability and interpretability. For example, when predicting subgrade displacement, data-driven models may not be able to accurately reveal the internal influence mechanism of factors such as freeze-thaw cycles and heavy traffic on subgrade displacement, thus affecting the reliability and credibility of their prediction results. In addition, when dealing with multi-field coupling problems, data-driven models often regard each physical field as an independent variable and do not fully consider the interaction and synergy effects between the temperature field, moisture field, and stress field, further limiting their application effects in complex engineering environments.

[0005] To solve this problem, a new method, namely Physics-Informed Neural Networks (PINN), has been proposed in recent years. By embedding physical equations into the loss function of a neural network, PINN enables the model to learn data and physical laws simultaneously during training. This method has improved the generalization ability and interpretability of the model to a certain extent. However, when dealing with multi-field coupling problems, due to the complexity of physical equations, the training of the PINN model is difficult, and it has a strong dependence on initial conditions and boundary conditions.

[0006] Catastrophes in engineering practice are usually caused by a combination of multiple factors. Traditional prediction methods still face some difficulties in dealing with such catastrophe problems with multi-field coupling and time-series non-linearity: Numerical models based on physical mechanisms (such as the finite element method) are limited by one-dimensional assumptions and steady-state simplifications, making it difficult to capture the long-term cumulative effects of freeze-thaw cycles and dynamic loads; while data-driven models (such as deep learning), although good at time-series modeling, lack physical constraints and dependence on measured data, resulting in insufficient generalization ability and lack of interpretability.

[0007] In response to the above problems, in recent years, LSTM (Long Short-Term Memory network) has shown unique advantages in the field of civil engineering health monitoring. Its gating mechanism can effectively capture time-series dependence relationships and has been successfully applied to prediction tasks such as bridge vibration and slope displacement. However, existing research mostly focuses on a single physical field (such as temperature or strain) and relies on large-scale measured data for training. More importantly, the essence of catastrophe evolution is a physical process of non-linear interaction between the temperature field (latent heat of phase change), moisture field (frost heave migration), and stress field (load transfer). The purely data-driven "black box" model cannot reveal the internal mechanism, which limits its engineering credibility. Summary of the Invention

[0008] To solve the technical problems existing in the above-mentioned prior art, the present invention proposes a method for predicting the internal depth displacement of a subgrade by integrating the multi-physical field coupling mechanism and the LSTM time-series prediction model. By embedding physical equations into the neural network loss function and integrating the multi-field coupling mechanism, the generalization ability and interpretability of the model are improved, and the subgrade displacement can be accurately predicted, providing a theoretical basis for the catastrophe prediction of low loess embankments in seasonal frozen regions.

[0009] To achieve the above object, the present invention provides a method for predicting the internal depth displacement of a subgrade by integrating the multi-physical field coupling mechanism and the LSTM time-series prediction model, including:

[0010] Respectively obtain the initial conditions of the temperature field, moisture field, and stress field in the area to be predicted;

[0011] Build a prediction model for the internal depth displacement of the subgrade, input the initial conditions into the prediction model for the internal depth displacement of the subgrade for prediction, and obtain the displacement prediction result;

[0012] Among them, the prediction model for the internal depth displacement of the subgrade is a physically constrained LSTM model, which includes several independent sub-networks. The characteristics of temperature, moisture, and stress are extracted through the independent sub-networks respectively, and the characteristics are fused to output the displacement prediction result.

[0013] Preferably, building the prediction model for the internal depth displacement of the subgrade includes:

[0014] Based on the theories of thermodynamics and frozen soil mechanics, build a one-dimensional unsteady multi-field coupling control equation set, where the one-dimensional unsteady multi-field coupling control equation set includes a temperature field control equation, a moisture field control equation, and a stress field control equation;

[0015] Discretize the one-dimensional unsteady multi-field coupling control equation set, and set the boundary conditions and initial parameters to obtain the prediction model for the internal depth displacement of the subgrade.

[0016] Preferably, the temperature field control equation characterizes the heat change during the freezing-thawing process of the soil by embedding the latent heat of phase change term; the moisture field control equation is based on the law of conservation of mass and introduces the water flux equation and the ice lens growth model to describe the moisture migration driven by frost heave; the stress field control equation adopts a non-linear elastoplastic constitutive model containing the frost heave stress term to characterize the stress-strain relationship of the soil under freeze-thaw cycles and load effects.

[0017] Preferably, the temperature field control equation is:

[0018]

[0019] In the formula, T is the temperature, z is the depth coordinate, t is the time, ρ is the soil density, k is the thermal conductivity, c is the specific heat capacity, θ is the water content, L = 334×10 3 J / kg is the latent heat of water-ice phase change, ε is the strain, θ i is the volume fraction of ice-water, ρ i is the ice density, and η is the annual dissipation coefficient;

[0020] The water flux equation is:

[0021]

[0022] In the formula, K(θ) is the permeability coefficient, D is the thermal gradient moisture migration coefficient, and Ψ is the matrix potential;

[0023] The ice lens growth model is:

[0024]

[0025] In the formula, k i is the ice segregation rate coefficient, ψ m is the matrix potential, ψ cr is the critical matrix potential;

[0026] The non-linear elastoplastic constitutive model is as follows:

[0027]

[0028] In the formula, σ(z,t) is the vertical stress, ε is the strain, E is the elastic modulus, σ 冻 is the frost heaving stress.

[0029] Preferably, the one-dimensional unsteady multi-field coupling control equation is constructed based on a two-way coupling mechanism, where the two-way coupling mechanism adjusts the interaction intensity of the temperature field, moisture field and stress field through a dynamic weight matrix, and the weight matrix is dynamically updated based on the freezing front movement rate and plastic strain accumulation.

[0030] Preferably, the discretization of the one-dimensional unsteady multi-field coupling control equations includes:

[0031] Discretize the spatial and time dimensions respectively by the finite difference method. Among them, the control equation is discretized by the central difference method, the time integration uses the implicit Euler method to ensure stability, and the coupling term realizes the interaction between fields through iterative update.

[0032] Preferably, inputting the initial conditions into the subgrade internal depth displacement prediction model for prediction includes:

[0033] Map the temperature field, moisture field and stress field to the independent sub-networks respectively through tensor decomposition, where the independent sub-networks include:

[0034] Temperature sub-network: The input features are the temperature gradient and the latent heat of phase change term;

[0035] Water molecule sub-network: The input features are the moisture migration rate and the moisture content gradient;

[0036] Stress sub-network: The input features are the frost heaving stress and the strain rate.

[0037] Preferably, the physical regularization loss function of the subgrade internal depth displacement prediction model is:

[0038] L total = L CE + L phy ;

[0039] In the formula, L total is the total loss function, L CEis the cross - entropy loss, L phy is the physical consistency constraint.

[0040] Preferably, the subgrade internal depth displacement prediction model adopts the Adam optimizer, the learning rate is set to 0.001, and Dropout regularization and L2 weight decay are added for training, and the number of hidden layer units in each independent sub - network is not exactly the same.

[0041] Compared with the prior art, the present invention has the following advantages and technical effects:

[0042] The method of the present invention obtains the data of the temperature field, moisture field and stress field of the subgrade through data collection and pre - processing; embeds the heat conduction equation and moisture migration equation as regularization terms into the LSTM loss function, and through physical constraint embedding, makes the model follow the law of physical conservation during the training process, improving the generalization ability and interpretability of the model; can comprehensively consider factors such as the latent heat of the water - ice box change, ice lens growth, energy conservation, dynamic drive and elastoplastic constitutive based on the multi - field coupling mechanism, accurately describe the interaction between the temperature field, moisture field and stress field, and further improve the prediction accuracy of the model; can dynamically quantify the interaction weights of the temperature - moisture - stress fields through the multi - field attention mechanism, and realize the switching of the dominant right between fields through a differentiable matrix, enabling the model to adaptively adjust the degree of attention to different physical fields and better capture the multi - field coupling effect; can independently model the characteristics of each physical field through the sub - field LSTM sub - network, and fuse the output through tensor decomposition, improving the adaptability of the model to complex working conditions; finally, achieve accurate prediction of the subgrade displacement, provide a theoretical basis and technical support for the disaster prediction of loess low embankments in seasonal frozen regions, effectively reduce the cost of subgrade disease repair, and ensure the service safety and economic sustainability of the road. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] The drawings forming a part of this application are used to provide a further understanding of this application. The schematic embodiments and descriptions thereof of this application are used to explain this application and do not constitute an improper limitation of this application. In the drawings:

[0044] Figure 1 is a schematic flow chart of the subgrade internal depth displacement prediction method that combines the multi - physical - field coupling mechanism and the LSTM time - series prediction model according to the embodiment of the present invention;

[0045] Figure 2 is a diagram of the change of attention weights according to the embodiment of the present invention;

[0046] Figure 3 is a prediction comparison diagram according to the embodiment of the present invention;

[0047] Figure 4 is a warning schematic diagram according to the embodiment of the present invention;

[0048] Figure 5 Schematic diagram of the arrangement of subgrade sensors in the embodiments of the present invention;

[0049] Figure 6 Mechanism diagram of the mutual coupling of double fields among three fields in the embodiments of the present invention. Specific embodiments

[0050] It should be noted that, without conflict, the embodiments in this application and the features in the embodiments may be combined with each other. The following will describe this application in detail with reference to the drawings and in combination with the embodiments.

[0051] It should be noted that the steps shown in the flowchart of the drawings may be executed in a computer system such as a set of computer-executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than here.

[0052] Such as Figures 1 - 6 , the present invention proposes a method for predicting the internal depth displacement of the subgrade by integrating the multi-physical field coupling mechanism and the LSTM time series prediction model, including:

[0053] Respectively obtain the initial conditions of the temperature field, moisture field and stress field in the area to be predicted;

[0054] Construct a prediction model for the internal depth displacement of the subgrade, input the initial conditions into the prediction model for the internal depth displacement of the subgrade for prediction, and obtain the displacement prediction result;

[0055] Among them, the prediction model for the internal depth displacement of the subgrade is a physically constrained LSTM model, including a number of independent sub-networks, which respectively extract the features of temperature, moisture and stress, fuse the features, and output the displacement prediction result.

[0056] Furthermore, constructing a prediction model for the internal depth displacement of the subgrade includes:

[0057] Based on the theories of thermodynamics and frozen soil mechanics, construct a one-dimensional unsteady multi-field coupling control equation set, where the one-dimensional unsteady multi-field coupling control equation set includes a temperature field control equation, a moisture field control equation and a stress field control equation;

[0058] Discretize the one-dimensional unsteady multi-field coupling control equation set, and set the boundary conditions and initial parameters to obtain the prediction model for the internal depth displacement of the subgrade.

[0059] Specifically, for the study of multi-field coupling, first, differential constraint relations of the temperature field (including latent heat conduction during phase change), moisture field (frost heave-driven migration), and stress field (elastoplastic constitutive model) are established based on the improved Harlan model; second, the bidirectional coupling mechanism of temperature gradient-driven moisture migration and frost heave stress feedback to the temperature field is analyzed, and the dynamic weights of multi-field interaction are quantified; finally, combined with codes and test data, the critical conditions of disasters under the combined action of multi-fields such as plastic strain accumulation and displacement rate threshold are defined.

[0060] Furthermore, the temperature field control equation characterizes the heat change during soil freezing and thawing processes by embedding the latent heat term of phase change; the moisture field control equation is based on the law of conservation of mass and introduces the ice lens growth model to describe frost heave-driven moisture migration; the stress field control equation adopts a nonlinear elastoplastic constitutive model containing the frost heave stress term to characterize the stress-strain relationship of soil under freeze-thaw cycles and load effects.

[0061] Specifically,

[0062] (1) Temperature field (including heat conduction during phase change):

[0063] Considering the latent heat effect of phase change during soil freezing and thawing processes, the temperature field control equation can be expressed as:

[0064]

[0065] In the formula, T(z,t) is the temperature (°C), z is the depth coordinate (m), t is the time (s); ρ is the soil density (kg / m 3 ), k is the thermal conductivity (W / (m·K)), which has a linear relationship with the water content θ, c is the specific heat capacity, ρ i is the ice density:

[0066] k0(1 + 0.05θ), k0 = 1.2(2);

[0067] In the formula, L = 334×10 3 J / kg is the latent heat of water-ice phase change; η is the annual dissipation coefficient (Pa·s); ε is the strain; θ i is the ice volume fraction, which is determined by the freezing characteristic curve:

[0068]

[0069] In the formula, T f is the freezing temperature, taken as -1°C; θ0 is the initial unfrozen water content.

[0070] (2) Moisture field (frost heave-driven migration):

[0071] In the moisture field, considering mass conservation and ice lens growth dynamics, the evolution of the moisture field is driven by both unfrozen water migration and ice segregation. Based on the law of mass conservation, the total water content: θ = θ u + θ i , θ u is the unfrozen water content, and θ i is the ice volume fraction. The mass conservation equation is reconstructed for the entire moisture migration and phase change process.

[0072] Among them, the mass conservation equation is:

[0073]

[0074] This equation represents that within a unit of time, the change in the volume fraction of water in the soil (θ u and θ i ) is equal to the divergence of the water flux (q), where θ u is the volume fraction of non-ice water, and θ i is the volume fraction of ice water, represents the divergence of the water flux.

[0075] The ice lens growth model can be based on Miller's freezing theory. The ice segregation rate is driven by the matric potential ψ m and is related to the critical matric potential ψ cr :

[0076]

[0077] In the formula, k i is the ice segregation rate coefficient (s-1), (x) + = max(x, 0) indicates that ice segregation occurs only when the matric potential exceeds the critical value; the critical matric potential ψ cr takes a typical value of 1×10 -4 .

[0078] At the same time, it is also necessary to consider the relationship between the matric potential and the moisture migration flux. The physical model of the matric potential in unsaturated soil is described by the vg model:

[0079]

[0080] In the formula, θ r is the residual water content, θ s is the saturated water content, and α, m, n are all soil parameters (m = 1 - 1 / n).

[0081] The water flux equation is:

[0082]

[0083] In the formula, K(θ) is the permeability coefficient, D is the heat gradient moisture migration coefficient, and the heat permeability coefficient K(θ) is introduced and the van Genuchten-Mualem model is adopted.

[0084]

[0085] In the formula, K S is the saturated permeability coefficient, and m = 0.37 is obtained from the soil-water characteristic curve test.

[0086] The coupled control equation is expressed as:

[0087]

[0088] (3) Stress field (elastoplastic constitutive):

[0089] Introduce a nonlinear elastoplastic model with a frost heave stress term:

[0090]

[0091] In the formula, σ(z,t) is the vertical stress (kPa), ε is the strain; E is the elastic modulus (MPa), which decays with the number of freeze-thaw cycles N:

[0092] E = E0(1 - 0.02N)·e (-αf) (11);

[0093] η = 50 kPa·s is the viscosity coefficient, which characterizes the creep characteristics of loess;

[0094] σ 冻 = βθ i is the frost heave stress (β = 0.15 MPa / %) (12).

[0095] Furthermore, based on the two-way coupling mechanism, the one-dimensional unsteady multi-field coupling control equation is constructed, where the two-way coupling mechanism is to adjust the interaction intensity of the temperature field, moisture field and stress field through a dynamic weight matrix, and the weight matrix is dynamically updated based on the freezing front movement rate and plastic strain accumulation.

[0096] Specifically, as Figure 6 , considering the two-way coupling mechanism: the temperature gradient drives moisture migration (heat-water coupling), and the moisture redistribution changes the thermal conductivity (water-heat feedback); the frost heave stress is affected by the moisture content (water-force coupling), and the stress change feeds back to the temperature field through plastic strain (force-heat coupling).

[0097] The coupled equations of the three fields are:

[0098]

[0099] Among them, the plastic strain rate Affects the temperature field through viscous dissipation; the temperature gradient in the moisture field Drives moisture migration, and the phase change term Reflects the moisture phase change at the freezing front; the water content θ in the stress field directly affects the frost heave stress βθ, and the elastic modulus E decays with the number of freeze-thaw cycles N.

[0100] Based on the elastoplastic constitutive model, when the frost heave stress and cyclic load act together, the plastic strain ε p And the accumulation of displacement rate v may trigger a catastrophe.

[0101] Furthermore, the discretization of the one-dimensional unsteady multi-field coupling control equations includes:

[0102] Discretize the spatial and time dimensions respectively by the finite difference method. Among them, the control equations are discretized by the central difference method, the time integration uses the implicit Euler method to ensure stability, and the coupling terms are realized by iterative update to achieve interaction between fields.

[0103] Specifically, the discretization method:

[0104] Discretize the control equations by the finite difference method. The spatial step size Δz = 0.1 m, the time step size Δt = 864 s (1 day). The control equations (temperature field, moisture field, stress field) are discretized by the central difference method, and the time integration uses the implicit Euler method to ensure stability. The coupling terms (such as the frost heave stress βθ) are realized by iterative update to achieve interaction between fields;

[0105] The time step size Δt = 864 s (1 day) satisfies the CFL stability condition: Where D max = 1×10 - 6 m 2 / s is the maximum diffusion coefficient.

[0106] Boundary conditions:

[0107] Temperature field: The surface temperature changes periodically:

[0108] T(0,t) = T0 + Asin(2πt / 365)(14);

[0109] In the formula, T0 = -5°C, A = 15°C;

[0110] Moisture field: The surface water content is constant, and the bottom is impermeable θ(0,t) = 15%,

[0111] Stress field: Dynamic load:

[0112] σ xy (t) = σ0sin(2πft)(15);

[0113] where σ0 = 50 kPa and the frequency f = 0.1 Hz.

[0114] (3) Initial conditions:

[0115] Temperature field: T(z, 0) = T0 + Asin(0) (uniform initial temperature);

[0116] Moisture field: θ(z, 0) = 15% (uniform moisture content);

[0117] Stress field: σ(z, 0) = 0 (no initial stress).

[0118] (4) Parameter values are shown in Table 1:

[0119] Table 1

[0120]

[0121] Furthermore, inputting the initial conditions into the subgrade internal depth displacement prediction model for prediction includes:

[0122] Mapping the temperature field, moisture field, and stress field to the independent sub-networks respectively through tensor decomposition, where the independent sub-networks include:

[0123] Temperature sub-network: The input features are the temperature gradient and the latent heat of phase change term;

[0124] Moisture sub-network: The input features are the moisture migration rate and the moisture content gradient;

[0125] Stress sub-network: The input features are the frost heave stress and the strain rate.

[0126] Specifically, based on Harlan's three-field coupling equation (13), mapping the temperature field T, moisture field θ, and stress field σ to the independent sub-networks through tensor decomposition: The input features are the temperature gradient and the latent heat of phase change term Temperature sub-network, moisture sub-network, the input features are the moisture migration rate q w and the moisture content gradient Stress sub-network, the input features are the frost heave stress σ 冻 = βθ and the strain rate

[0127] Field-split LSTM layer: Splitting the input features by physical field and inputting them into three LSTM sub-networks respectively:

[0128]

[0129]

[0130]

[0131] Tensor decomposition:

[0132] G = Τ × 1U (T) × 2U (θ) × 3U (σ) (19);

[0133] Where h T is the temperature sub - network, h θ is the moisture sub - network, h σ is the stress sub - network, G is the multi - field coupling tensor, σ f is the frost heaving stress, is the strain rate, 1U (T) is the input feature matrix corresponding to the temperature field, 2U (θ) is the input feature matrix corresponding to the moisture field, 3U (σ) is the input feature matrix corresponding to the stress field.

[0134] Such as Figure 2 , Dynamic weight allocation: The adaptability of the attention mechanism to physical laws is mainly reflected in aspects such as dynamic weight allocation, enhancing the interpretability of the model, and improving the generalization ability of the model. There are significant differences in weight allocation between the traditional softmax algorithm and the improved algorithm. The improved algorithm improves the expression ability, computational efficiency, and training stability of the model by introducing methods such as scaling factors, polynomial activation functions, and linear attention mechanisms. These improved algorithms have obvious advantages in dealing with large - scale data and complex tasks and can better meet the requirements of physical constraint models.

[0135] The attention mechanism adjusts the multi - field contribution through the coupling strength λ:

[0136] a t = Softmax(W a [h T , h θ , h σ )(20);

[0137] Where a t is the attention weight at time t, and W a is the attention weight matrix.

[0138] The attention matrix M eff = R λδ The coefficient λ of characterizes the coupling strength between the temperature field and the moisture field, and its element a i is dynamically adjusted through the freezing front movement rate to reflect the switching mechanism of the multi - field dominant period (such as the moisture - dominant period θ ≥ 0.68, the stress - dominant period θ ≥ 0.53.

[0139] The architecture of the prediction model for the internal depth displacement of the subgrade is as follows:

[0140] Input gate: Introduce physical gradient constraints:

[0141] Forget gate:

[0142] In the formula, f t is the output of the forget gate at time t, controlling the retention degree of the cell state C t-1 at the previous time; W f is the weight matrix of the forget gate for the concatenation of the hidden layer h t-1 and the current input x t ; U f is the weight matrix of the forget gate for the physical gradient term. Similar to the input gate, it incorporates physical constraints. F is the coupling equation; is the physical gradient, calculated by automatic differentiation.

[0143] Output gate:

[0144] In the formula, O t is the output of the output gate at time t, controlling the output degree of the current cell state C t to the hidden layer h t ; W o is the weight matrix of the output gate for the concatenation of the hidden layer h t-1 and the current input x t .

[0145] State update:

[0146] In the formula, c t is the updated cell state at time t, integrating historical information and the current input. ⊙ is the Hadamard product. f t ⊙c t-1 is the retained part of the cell state c t at the previous time controlled by the forget gate f t-1 ; i t ⊙tanh(·) is the added part of the current input information controlled by the input gate i t ; U c is the weight matrix for the physical gradient total in the state update, introducing physical constraints to participate in the state update.

[0147] Furthermore, the physical regularization loss function of the prediction model for the internal depth displacement of the subgrade is:

[0148] L total = L CE + L phy (25);

[0149] In the formula, L total is the total loss function, L CE is the cross-entropy loss, and L phy is the physical consistency constraint.

[0150] Specifically, the cross-entropy loss: the basic loss for the classification task:

[0151]

[0152] The physical consistency constraint: forces the predicted value to satisfy the governing equation:

[0153]

[0154] The total loss:

[0155] L total = L CE + L phy (28);

[0156] In the formula, λ1 = 0.5, λ2 = 0.3, determined by grid search; N is the number of samples, used for the statistics of batch samples when calculating the loss function, is the physical quantity predicted by the model, is the predicted temperature field variable, is related to the predicted temperature and the related source term, is the predicted strain, and D is the diffusion coefficient.

[0157] Furthermore, the subgrade internal depth displacement prediction model adopts the Adam optimizer, the learning rate is set to 0.001, and Dropout regularization and L2 weight decay are added for training, and the number of hidden layer units in each independent sub-network is not exactly the same.

[0158] Specifically, in this embodiment, the number of hidden layer units in each independent sub-network: the number of hidden layer units in the temperature field LSTM is 32, the number of hidden layer units in the moisture field LSTM is 32, and the number of hidden layer units in the stress field LSTM is 16.

[0159] Optimizer: Adam (learning rate η = 0.001, decay rate β1 = 0.9, β2 = 0.999);

[0160] Regularization: Dropout (ratio 0.3), L2 weight decay (coefficient 1×10 -4 ).

[0161] In this embodiment, through data collection and preprocessing, data on the temperature field, moisture field, and stress field of the subgrade are obtained; the heat conduction equation and moisture migration equation are embedded as regularization terms into the LSTM loss function, and through physical constraint embedding, the model follows the law of physical conservation during the training process, improving the generalization ability and interpretability of the model; based on the multi-field coupling mechanism, factors such as the latent heat of the water-cooled transformer, ice lens growth, energy conservation, dynamic drive, and elastoplastic constitutive are comprehensively considered to accurately describe the interaction between the temperature field, moisture field, and stress field, further improving the prediction accuracy of the model; through the multi-field attention mechanism, the interaction weights of the temperature-moisture-stress field are dynamically quantified, and the field dominance switch is realized through a differentiable matrix, enabling the model to adaptively adjust the degree of attention to different physical fields and better capture the multi-field coupling effect; through the sub-field LSTM sub-network, the characteristics of each physical field are independently modeled, and the output is fused through tensor decomposition to improve the adaptability of the model to complex working conditions; finally, accurate prediction of the subgrade displacement is achieved, providing a theoretical basis and technical support for the disaster prediction of loess low embankments in seasonal frozen regions, effectively reducing the repair cost of subgrade diseases, and ensuring the service safety and economic sustainability of the road.

[0162] The above is only a preferred specific embodiment of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed in the present application should be covered by the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for predicting the internal depth displacement of a roadbed by integrating the coupling mechanism of multiple physical fields and an LSTM time series prediction model, characterized in that Including: Respectively obtain the initial conditions of the temperature field, moisture field, and stress field within the area to be predicted; Construct a prediction model for the internal depth displacement of the subgrade, input the initial conditions into the prediction model for the internal depth displacement of the subgrade for prediction, and obtain the displacement prediction result; Among them, the prediction model for the internal depth displacement of the subgrade is a physically constrained LSTM model, including a number of independent sub-networks, extracting the characteristics of temperature, moisture, and stress through the independent sub-networks respectively, fusing the characteristics, and outputting the displacement prediction result.

2. The method for predicting the internal depth displacement of the subgrade by integrating the multi-physical field coupling mechanism and the LSTM time series prediction model according to claim 1, characterized in that Constructing a prediction model for the internal depth displacement of the subgrade includes: Based on the theories of thermodynamics and frozen soil mechanics, construct a one-dimensional unsteady multi-field coupling control equation set, where the one-dimensional unsteady multi-field coupling control equation set includes a temperature field control equation, a moisture field control equation, and a stress field control equation; Discretize the one-dimensional unsteady multi-field coupling control equation set, and set boundary conditions and initial parameters to obtain the prediction model for the internal depth displacement of the subgrade.

3. The method for predicting the internal depth displacement of a subgrade by integrating the multi-physical field coupling mechanism and the LSTM time series prediction model according to claim 2, characterized in that, The temperature field control equation characterizes the heat change during the freezing-thawing process of the soil by embedding the latent heat of phase change term; the moisture field control equation is based on the law of conservation of mass and introduces the water flux equation and the ice lens growth model to describe the moisture migration driven by frost heave; the stress field control equation adopts a non-linear elastoplastic constitutive model containing a frost heave stress term to characterize the stress-strain relationship of the soil under freeze-thaw cycles and load effects.

4. The method for predicting the internal depth displacement of subgrade by integrating the multi-physical field coupling mechanism and the LSTM time series prediction model according to claim 3, characterized in that, The temperature field control equation is: where T is the temperature, z is the depth coordinate, t is the time, ρ is the soil density, k is the thermal conductivity, c is the specific heat capacity, θ is the water content, L = 334×10 3 J / kg is the latent heat of water-ice phase change, ε is the strain, θ i is the volume fraction of ice-water, ρ i is the ice density, and η is the annual dissipation coefficient; The water flux equation is: In the formula, K(θ) is the permeability coefficient, D is the thermal gradient moisture migration coefficient, and ψ is the matrix potential; The ice lens growth model is: where k i is the ice segregation rate coefficient, ψ m is the matric potential, and ψ cr is the critical matric potential; The non-linear elastoplastic constitutive model is: where σ(z,t) is the vertical stress, ε is the strain, E is the elastic modulus, and σ 冻 is the frost heaving stress.

5. The method for predicting the internal depth displacement of the subgrade by integrating the multi-physical field coupling mechanism and the LSTM time series prediction model according to claim 4, characterized in that, Construct the one-dimensional unsteady multi-field coupling control equation based on a two-way coupling mechanism, where the two-way coupling mechanism is to adjust the interaction intensity of the temperature field, moisture field, and stress field through a dynamic weight matrix, and the weight matrix is dynamically updated based on the freezing front movement rate and plastic strain accumulation.

6. The method for predicting the internal depth displacement of the subgrade by integrating the multi-physical field coupling mechanism and the LSTM time series prediction model according to claim 2, wherein Discretizing the one-dimensional unsteady multi-field coupling control equation set includes: Discretize the spatial and time dimensions respectively by the finite difference method, where the control equation is discretized by the central difference method, the time integration uses the implicit Euler method to ensure stability, and the coupling term realizes the interaction between fields through iterative update.

7. The method for predicting the internal depth displacement of a roadbed by integrating the multi-physical field coupling mechanism and the LSTM time series prediction model according to claim 1, wherein Inputting the initial conditions into the prediction model for the internal depth displacement of the subgrade for prediction includes: Map the temperature field, moisture field, and stress field to the independent sub-networks respectively through tensor decomposition, where the independent sub-networks include: Temperature sub-network: The input features are the temperature gradient and the latent heat of phase change term; Water molecule sub-network: The input features are the moisture migration rate and the moisture content gradient; Stress sub-network: The input features are the frost heave stress and the strain rate.

8. The method for predicting the internal depth displacement of the subgrade by integrating the multi-physical field coupling mechanism and the LSTM time series prediction model according to claim 1, characterized in that, The physical regularization loss function of the prediction model for the internal depth displacement of the subgrade is: L total = L CE + L phy ; where, L total is the total loss function, L CE is the cross-entropy loss, and L phy is the physical consistency constraint.

9. The method for predicting the internal depth displacement of a roadbed by integrating the multi-physical field coupling mechanism and the LSTM time series prediction model according to claim 8, characterized in that, The prediction model for the internal depth displacement of the subgrade uses the Adam optimizer, the learning rate is set to 0.001, and Dropout regularization and L2 weight decay are added for training, and the number of hidden layer units in each independent sub-network is not exactly the same.

Images