A Dynamic Prediction Method for Tunnel Displacement Field Based on Physical Information Neural Network

Abstract

This invention discloses a dynamic prediction method for tunnel displacement fields based on a physical information neural network, belonging to the field of tunnel engineering technology, and serving real-time deformation prediction during tunnel excavation. The invention first uses historical excavation data to generate timestamped displacement and strain field sequences, and trains a PINN physical inference model and a PLSTM temporal recursive model respectively. As the actual excavation progresses, the overall displacement and strain are rapidly calculated based on the geological parameters of the current step, and then input into the temporal recursive model to predict the displacement field of the next excavation step. Simultaneously, the mean square value and second derivative of each parameter along the excavation step sequence are analyzed to automatically identify floating and unstable parameters, and four sets of composite geological scenarios are constructed accordingly. These scenarios drive the prediction of the corresponding displacement field set output by the pipeline in parallel, forming a displacement envelope. This invention achieves physically reasonable and risk-quantified dynamic prediction of displacement fields during the excavation process, providing a quantitative basis for early warning and support decisions.

Description

Technical Field

[0001] This invention relates to the field of tunnel engineering technology, specifically to a dynamic prediction method for tunnel displacement field based on physical information neural networks. Background Technology

[0002] As tunnel engineering progresses towards deeper, longer distances, and more complex geological conditions, automated monitoring systems and geological forecasting technologies deployed during construction have accumulated massive amounts of time-series data on displacement, stress, and rock mass parameters. Simultaneously, the widespread application of numerical simulation software has made inverting continuous mechanical fields from discrete exploration data a routine practice. At the computational level, the maturity of Physical Information Neural Networks (PINNs) provides a new paradigm for embedding geotechnical control equations and boundary conditions as regularization constraints into network training, enabling data-driven models to naturally satisfy the laws of solid mechanics. The long-term dependency capture capability exhibited by Long Short-Term Memory Networks (PLSTMs) in sequence modeling provides an effective tool for capturing the dynamic processes of deformation accumulation and stress redistribution caused by multiple excavation steps. Furthermore, the spatial variability of geotechnical parameters and the progressive degradation caused by excavation disturbances have attracted widespread attention in the engineering community. Data-driven parameter sensitivity screening methods based on statistical characteristics and differential analysis are increasingly becoming an important foundation for risk quantification. The convergence of the aforementioned data conditions, physical coding model, and temporal reasoning capabilities constitutes the technical background for the development of a dynamic prediction method for tunnel displacement fields that integrates PINN instantaneous physical decomposition, PLSTM dynamic recursion, and multi-scenario parameter perturbation prediction.

[0003] In the prior art, document CN119004629A discloses a method for analyzing the stress field of tunnel surrounding rock based on a physical information neural network. This method effectively combines known information data with physical knowledge to predict the elastoplastic stress field of tunnel surrounding rock. The method includes: Step 1, constructing an artificial neural network (ANN) framework; Step 2, generating physical driving information based on the Mohr-Coulomb model; Step 3, generating data driving information based on adaptive strain sampling points; Step 4, constructing a multi-objective loss function to train the physical information neural network; and Step 5, training the constructed physical information neural network to solve for the stress field of the tunnel surrounding rock.

[0004] Although the published technical documents have achieved the construction of the surrounding rock stress field and provided data guidance for excavation projects, the actual excavation process is not an ideal stable environment. Many situations that cannot be simulated will occur under complex geological conditions. Therefore, the technical effects of the published documents provide limited data for guidance during the process and cannot better guide the excavation process.

[0005] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to provide a dynamic prediction method for tunnel displacement field based on physical information neural network, so as to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A dynamic prediction method for tunnel displacement field based on physical information neural network, comprising the following steps: Step 1: Obtain the original dataset through the historical excavation process. The original dataset includes tunnel displacement field, stress-strain field and geological data. Input the original data into simulation software for simulation inversion to obtain time series displacement field and strain field data. Step 2: Using the geological data corresponding to each excavation step as the first sample and the corresponding displacement field and strain field data as labels, train in the PINN model to obtain the first judgment model. Using the time series displacement field and strain field data as the second sample and the corresponding displacement field data as samples, train in the P-LSTM model to obtain the second judgment model. Step 3: Obtain the original dataset of the actual excavation process, perform simulation inversion using the geological data in it, and use the inversion results to obtain the current first displacement component and the current first strain variable in the first judgment model. Combine the current first displacement component and the current first strain variable with the tunnel displacement field and stress-strain field and input them into the second judgment model to obtain the current second displacement field of the next excavation step. Step 4: Based on the time sequence of each parameter type in the geological data of each excavation step in the actual excavation process, form a parameter sequence, and select floating data and unstable data according to the numerical changes in each parameter sequence; Step 5: Adjust the geological data according to the data range in the floating data and the second derivative value in the unstable data to obtain several geological data sets. Repeat step 3 for each geological data set to obtain several predicted second displacement fields and output them.

[0008] Furthermore, a raw dataset is obtained through the historical tunnel excavation process. This dataset includes the tunnel displacement field, stress-strain field, and corresponding timestamps and geological data at various locations during each excavation. This data is then input into numerical simulation software for dynamic simulation and inversion. The geological data includes elastic modulus, Poisson's ratio, cohesion, internal friction angle, tensile strength, density, initial ground stress components, and shear stress components. The geological data required for the dynamic simulation is obtained by setting a time window, the length of which is the duration of several excavation steps. The displacement field and strain field data within each time window are obtained through the simulation process. The displacement field and strain field data are data sequences marked with timestamps. The displacement field data represents displacement components, and the strain field data represents strain variables.

[0009] Furthermore, the geological data of each excavation step during the simulation inversion process is read to form the first sample. The displacement component and strain corresponding to the excavation step are used as labels and input into the PINN model for training. The trained model is labeled as the first judgment model, and the output is the first displacement component and the first strain of the excavation step.

[0010] Furthermore, several consecutive displacement and strain field data are organized into a second sample, and the first displacement field data after this sample is used as the label. The sample is then input into the P-LSTM model for training. The trained model is labeled as the tunnel displacement field model, and the output is the second displacement field after this excavation step. The trained model is then labeled as the second judgment model.

[0011] Furthermore, during the actual excavation process, the tunnel displacement field and stress-strain field of each excavation step are recorded in chronological order, and the actual displacement field and strain field data are simulated and input into the first judgment model to obtain the current first displacement component and the current first strain. Input the current first displacement component and the current first strain as the current displacement field and strain field data into the second judgment model to obtain the current second displacement field after this excavation step.

[0012] Furthermore, all geological data during each excavation step are acquired, and corresponding parameter sequences are formed according to the corresponding data types and acquisition time order. The mean square value and second derivative value within each parameter sequence are obtained. The second derivative value is the last second derivative value calculated with the latest geological data. The parameter sequence with the largest mean square value is identified and labeled as floating data, and the parameter sequence with the largest absolute value of the second derivative value is identified and labeled as unstable data.

[0013] Furthermore, the fluctuation range of the data within the floating sequence is obtained, and its data limit is calculated based on the second-order derivative of the unstable data. The calculation logic is as follows: Using the current excavation step value as a known point, the limit data is obtained twice based on the second-order differential value; Divide the numerical range within the floating range into three equal parts, and combine the upper and lower limits of the floating range to form a total of four data points.

[0014] Furthermore, the floating and unstable data in the current excavation step are adjusted separately to obtain four geological data sets. The adjustment logic is as follows: During the actual excavation, the four data points formed by the floating range are replaced with the parameter values ​​corresponding to the geological data used in the simulation inversion, and the replacement is carried out four times in total to form four adjusted geological data. Then, the limit data of the instability data is replaced with the corresponding parameter values ​​in these four adjusted geological data. Furthermore, the four geological data sets are simulated and inverted respectively, and input into the first judgment model to obtain four predicted first displacement components and predicted first strain. The four first components are then input into the second judgment model to obtain four predicted second displacement fields. The four predicted second displacement fields and the current second displacement field are output respectively.

[0015] Compared with the prior art, the beneficial effects of the present invention are: This invention trains a physical inferrer that directly outputs full-field displacement and strain that satisfy mechanical conservation from geological parameters by establishing time-series field data through numerical simulation inversion. This inferrer is seamlessly linked with a time-series predictor that recursively predicts future deformation based on historical sequences. This achieves a closed-loop process that continuously calculates the current full-field displacement in real time as excavation progresses and predicts the displacement field of the next excavation step one step ahead. Based on this, the invention automatically identifies floating and unstable parameters using the mean square value and second-order derivative of the geological parameter sequence. It constructs four sets of composite geological scenarios covering fluctuation ranges and extreme deterioration, and drives isomorphic prediction pipelines in parallel to generate corresponding predicted displacement sets. This transforms the propagation of invisible rock mass property uncertainties into multi-scenario displacement envelopes that can be compared laterally. This transforms tunnel displacement prediction from a single numerical extrapolation relying on human experience to a real-time quantitative analysis system that ensures the rationality of extrapolation by physical constraints, quantifies the risk range of parameter perturbations, and can directly provide the most unfavorable deformation warning for support adjustment and step distance decisions. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the overall method flow of the present invention; Figure 2 This is a schematic diagram of the PINN neural network model structure of the present invention; Figure 3 A schematic diagram comparing the simulation inversion results of this invention embodiment, wherein (a) is the displacement cloud map of the simulation inversion and (b) is the actual displacement cloud map; Figure 4This is a schematic diagram of the dynamic tunnel displacement field prediction results (at different excavation steps) in an embodiment of the present invention. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0018] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0019] Example: Please see Figure 1 The present invention provides a technical solution: A dynamic prediction method for tunnel displacement field based on physical information neural network, comprising the following steps: Step 1: Obtain the original dataset through the historical excavation process. The original dataset includes tunnel displacement field, stress-strain field and geological data. Input the original data into simulation software for simulation inversion to obtain time series displacement field and strain field data. Step 1 includes the following: The original dataset is obtained through historical tunnel excavation processes. This dataset includes the tunnel displacement field, stress-strain field, and corresponding timestamps and geological data at various locations during each excavation. This data is then input into numerical simulation software for dynamic simulation and inversion. The geological data includes elastic modulus, Poisson's ratio, cohesion, internal friction angle, tensile strength, density, initial ground stress components, and shear stress components. The geological data required for the dynamic simulation is obtained by setting time windows, the length of which is the duration of several excavation steps. Displacement and strain field data within each time window are obtained through the simulation process. These displacement and strain field data are time-stamped data sequences; the displacement field data represents displacement components, and the strain field data represents strain variables.

[0020] By inputting discrete monitoring displacement, stress, and geological survey data collected during the tunnel's historical excavation process into numerical simulation software for dynamic inversion, a spatiotemporal sequence of displacement components and strain variables with timestamps, strictly synchronized with the construction steps, was generated. This compensated for the lack of comprehensive information caused by the sparse on-site measuring points, providing high-quality training samples and labels covering the entire excavation process and ensuring a continuous physical field for the deep network. Explicitly pairing geological parameters with the mechanical response within each time window organized the mapping relationship between rock mass properties and deformation into a data structure that the network could learn, solving the problem that heterogeneous and unstructured on-site data could not directly drive the physical information model.

[0021] In a preferred embodiment, the displacement field data includes longitudinal displacement components, horizontal displacement components, and vertical settlement displacement components. The strain field data includes normal strain components and shear strain components in three directions.

[0022] As a preferred embodiment, simulation inversion was performed using CASRock software, and a three-dimensional geological model was established using Rhinoceros software. The model dimensions were X×Y×Z=113.3 m. 120 m The geological data has a mesh size of 136.35 m, 732,000 elements, and 750,666 nodes. The parameters were imported into the numerical simulation software CASRock, and Table 1 details the parameters of each element. Heterogeneous numerical simulations were performed on the tunnel simulation mesh model using the heterogeneous option in CASRock. The tunnel excavation process consisted of 20 steps, each with a length of 6 m, for a total excavation of 120 m. The displacement and stress fields of the tunnel were obtained through simulation.

[0023] Table 1 Geological Data Step 2: Using the geological data corresponding to each excavation step as the first sample and the corresponding displacement field and strain field data as labels, train in the PINN model to obtain the first judgment model. Using the time series displacement field and strain field data as the second sample and the corresponding displacement field data as samples, train in the P-LSTM model to obtain the second judgment model. Step 2 includes the following: Step 201: Read the geological data of each excavation step during the simulation inversion process to form the first sample. Use the displacement component and strain corresponding to the excavation step as labels and input them into the PINN model for training. Label the trained model as the first judgment model and output the first displacement component and first strain of the excavation step.

[0024] Using geological parameters such as elastic modulus, cohesion, and geostress components corresponding to each excavation step as inputs, and displacement components and strain variables generated by numerical simulation as monitoring signals, the model is trained using PINN, which embeds rock mass equilibrium equations and boundary conditions into the loss function. The resulting first judgment model can directly infer the full-field displacement and strain responses that strictly satisfy solid mechanics constraints from geological parameters. This physical embedding allows the model to maintain the physical rationality of extrapolation even when encountering unseen geological conditions, compressing the complex nonlinear mapping from rock mass properties to the deformation field into a differentiable and fast inferrer, providing a reliable current-state solution capability for real-time prediction.

[0025] As a preferred embodiment, a physical information neural network architecture is adopted. Its core lies in establishing a direct mapping from geological parameters and spatial location to full-section displacement and strain, while embedding the mechanical control equations of the tunnel surrounding rock as hard constraints into the network training process. In terms of network structure, a fully connected feedforward neural network is constructed. The input layer simultaneously receives the three-dimensional spatial coordinates of any point within the tunnel cross-section (longitudinal coordinates along the excavation direction, vertical coordinates in the vertical direction, and transverse coordinates in the horizontal direction) and a set of geological parameters of the surrounding rock exposed at that excavation step. These parameters specifically include elastic modulus, Poisson's ratio, cohesion, internal friction angle, tensile strength, density, and initial in-situ stress components and shear stress components. These parameters are replicated and expanded to match the number of coordinate points before being fed into the network.

[0026] The hidden layer consists of five layers, each containing 64 neurons. The activation function is the hyperbolic tangent function to ensure the high-order continuous differentiability of the output displacement field, thus enabling accurate calculation of strain and stress. The output layer has only three neurons, corresponding to the longitudinal displacement component, vertical settlement displacement component, and horizontal displacement component of the corresponding spatial point, respectively. The strain components are not directly output by the network but are obtained by calculating the partial derivatives of the output displacement with spatial coordinates through an automatic differentiation mechanism. This yields three normal strain components and three shear strain components, ensuring that the displacement and strain strictly satisfy the geometric equations and maintain deformation compatibility. The physical information is introduced by using the strain components obtained from automatic differentiation, combined with the elastic modulus and Poisson's ratio from the input geological parameters, to calculate six stress components according to the generalized Hooke's law. Then, the partial derivatives of these stress components with spatial coordinates are calculated, and the static equilibrium equation residuals are constructed. Ideally, these residuals should be zero.

[0027] The loss function during training consists of two weighted parts. One part is the data fitting loss, which includes the mean square error between the network output displacement and the numerical simulation label displacement, as well as the mean square error between the strain obtained by automatic differentiation and the label strain. The other part is the physical information loss, which is the mean square value of the residual of the aforementioned static equilibrium equation over the entire computational domain. The weight ratio of the two parts is set to 10:1, so that the model faithfully reflects the simulation data while strongly constraining the output field to satisfy the linear elastic mechanical equilibrium condition.

[0028] The training samples for each excavation step are generated by uniformly and randomly collecting tens of thousands of spatial coordinate points from the numerical simulation displacement and strain fields corresponding to that step, extracting the coordinates, labeled displacement components, and labeled strain components of each point, and recording the geological parameters of that step as common inputs to form a training batch.

[0029] The training employed an adaptive moment estimation optimizer with an initial learning rate of 0.001. The learning rate decreased to 7 / 10 of the previous stage every 2000 training iterations, for a total of 20,000 iterations. All sample points were used in each iteration to ensure full convergence. The physical information neural network model obtained through this training process was designated as the first judgment model. In practical use, given the geological parameters of a new excavation step, simply generating a spatial coordinate grid on the section to be predicted and inputting it into the model simultaneously outputs three displacement components across the entire field, and then automatically differentiates to obtain the corresponding six strain components. This approach fully embeds the inherent physical relationship between the displacement field, strain field, and geological parameters into the model's reasoning logic. That is, geological parameters determine the stiffness and strength characteristics of the medium, and strain is mapped to stress through constitutive relations. The stress, in turn, must satisfy the equilibrium differential equations. These relationships are simultaneously enforced during training. Therefore, the displacement and strain output by the model are not only superficially related to the input geological conditions but are also deeply controlled by the mechanical equilibrium mechanism of the surrounding rock. Therefore, even in areas lacking sufficient monitoring data or encountering combinations of geological parameters not found in the training data, the model can still provide physically reasonable and continuous prediction results, providing a solid and reliable basis for the current mechanical state for subsequent time-series recursive predictions, and greatly enhancing the engineering usability and extrapolation reliability of dynamic predictions.

[0030] Step 202: Organize several consecutive displacement and strain field data into a second sample, and use the first displacement field data after this sample as the label to input into the P-LSTM model for training. The trained model is labeled as the tunnel displacement field model, and the output is the second displacement field after this excavation step. The trained model is labeled as the second judgment model.

[0031] The continuous displacement and strain field time series are organized into input-output sample pairs. The PLSTM gating mechanism is used to capture the temporal dependence of tunnel displacement accumulation and release with multiple excavation steps. The trained second judgment model learns the dynamic evolution law of displacement field in the next excavation step from the recent mechanical state. This time series predictor encodes the deformation trend and stress adjustment process contained in the simulation data into a generalizable recursive pattern, complementing the aforementioned physical inference model. One is responsible for mapping geological conditions to mechanical state in real time, while the other is responsible for extrapolating the time series of mechanical state to the future, forming a complete dynamic prediction dual engine.

[0032] As a preferred embodiment, a physical sequence long short-term memory network architecture is adopted. The core idea is to enable the model to learn the dynamic recursive law of tunnel deformation with the construction process from the joint time series of displacement field and strain field of multiple consecutive excavation steps, and establish a direct mapping between past mechanical state and future displacement field, thereby getting rid of the dependence on iterative solution of complex dynamic equations.

[0033] In terms of network structure, a sequence input preprocessing layer is first set up to flatten the complete full-section displacement and strain field data of each historical excavation step into a one-dimensional vector. This vector contains three displacement components (longitudinal displacement, vertical settlement, and horizontal displacement) and six strain components (three normal strains and three shear strains) at each spatial grid point. The flattened vectors of different time steps are arranged in the order of excavation to form the input sequence. The sequence length is set to five consecutive excavation steps to balance the sufficiency of capturing time-series dependencies with computational efficiency, enabling the network to perceive the stress redistribution and deformation accumulation process caused by excavation. After the sequence preprocessing layer, two stacked layers of long short-term memory network units are connected. Each layer contains 128 memory units, and the activation function is hyperbolic tangent. A random deactivation mechanism with a dropout probability of 0.2 is introduced between layers to suppress overfitting to noise in the training sequence. The forget gate, input gate, and output gate structure of the long short-term memory network allows deformation trend information from early excavation steps to be selectively retained, while recent perturbation information is enhanced, thereby accurately characterizing the time delay effect and nonlinear acceleration features in displacement evolution. The hidden state of the last time step output by the sequence coding layer is fed into a fully connected decoder. This decoder consists of two hidden layers with 256 and 128 neurons per layer, respectively, and also uses hyperbolic tangent activation. The final output layer has the same number of neurons as the dimension of the flattened displacement field vector, directly providing the predicted values ​​of all grid points for the three displacement components of the full cross-section for the next excavation step. The training data is constructed by extracting the displacement and strain fields of five consecutive excavation steps from the complete excavation time series data obtained from historical numerical simulation inversion, using a sliding window as input samples. The displacement field of the sixth excavation step is used as the label. This process is repeated throughout the entire construction sequence to generate tens of thousands of sample pairs, which are then divided into training and validation sets according to the construction stage. The loss function uses the mean square error between the predicted displacement components and the numerically simulated labeled displacement components to measure the overall prediction accuracy across the entire cross-section. It does not require embedding explicit physical equations because the input includes both displacement and strain fields, implicitly containing deformation compatibility information related to the geometric equations. Sequence modeling implicitly learns the deformation transfer patterns caused by stress balance adjustments from the data. The training process uses an adaptive moment estimation optimizer with an initial learning rate of 0.001, decaying to 80% of the previous value every 3000 training epochs for a total of 5000 epochs. In each epoch, all training samples are fed into the network to update parameters, and validation set errors are monitored to prevent overfitting. After training, the model is calibrated as the second judgment model. In actual use, it receives the displacement and strain field sequences from the first judgment model's step-by-step calculations or the monitoring system's data from the five most recent excavation steps. After inputting these sequences into the model, it can forward one step and output the predicted displacement field value for the next excavation step.This approach eliminates the reliance on pre-assumed rock mass constitutive parameters and complex incremental iterative calculations for tunnel displacement prediction. Instead, it adaptively captures the deformation propagation pattern triggered by excavation unloading directly from the field sequence that fully reflects the recent mechanical response of the rock mass. The prediction results inherit the geological variations in the input sequence and reflect the accelerating displacement trend caused by the gradual accumulation of surrounding rock damage. When combined with the physically reasonable initial state provided by the first judgment model, the entire dynamic prediction chain forms a closed loop: "Geological parameters are used to physically calculate the current overall field state, and the sequence model recursively predicts future deformations over time." Ultimately, this provides the construction site with real-time displacement prediction capabilities that combine mechanical consistency with dynamic evolution visualization.

[0034] Step 3: Obtain the original dataset of the actual excavation process, perform simulation inversion using the geological data in it, and use the inversion results to obtain the current first displacement component and the current first strain variable in the first judgment model. Combine the current first displacement component and the current first strain variable with the tunnel displacement field and stress-strain field and input them into the second judgment model to obtain the current second displacement field of the next excavation step. Step 3 includes the following: In the actual excavation process, the tunnel displacement field and stress-strain field of each excavation step are recorded in chronological order. The actual displacement field and strain field data are simulated and input into the first judgment model to obtain the current first displacement component and the current first strain. During the actual excavation process, the geological parameters of the newly exposed working face are numerically simulated and then fed into the first judgment model. This model instantly calculates the physical field—the first displacement component and the first strain—consistent with the current geological and stress history, transforming the discrete geological description into continuous state quantities with full-field accuracy and mechanical consistency. This transformation ensures that the starting point for real-time prediction no longer depends on sparse monitoring displacement interpolation, thereby eliminating initial state distortion caused by spatial undersampling and ensuring that subsequent time-series predictions are based on a reliable physical foundation.

[0035] Input the current first displacement component and the current first strain as the current displacement field and strain field data into the second judgment model to obtain the current second displacement field after this excavation step.

[0036] The current displacement component and strain output by the first judgment model are directly fed into the second judgment model as the initial state, activating the trained temporal recursive logic. This forward pushes forward one step to obtain the predicted displacement field for the next excavation step, achieving a seamless connection between the physical inference engine and the data-driven predictor. This connection allows for dynamic updates to the prediction results each time new geological and monitoring information is obtained, forming an online closed loop of "sensing geology → solving the current full field → predicting future displacement," providing real-time quantitative criteria for construction risks.

[0037] Step 4: Based on the time sequence of each parameter type in the geological data of each excavation step in the actual excavation process, form a parameter sequence, and select floating data and unstable data according to the numerical changes in each parameter sequence; Step 4 includes the following: All geological data during each excavation step are acquired, and corresponding parameter sequences are formed according to the data type and acquisition time order. The mean square value and second derivative value within each parameter sequence are obtained. The second derivative value is the last second derivative value calculated with the latest geological data. The parameter sequence with the largest mean square value is identified and labeled as floating data, and the parameter sequence with the largest absolute value of the second derivative value is identified and labeled as unstable data.

[0038] In a preferred embodiment, the parameter sequence includes an elastic modulus parameter sequence, a Poisson's ratio parameter sequence, a cohesion parameter sequence, an internal friction angle parameter sequence, a tensile strength parameter sequence, a density parameter sequence, an initial ground stress component parameter sequence, and a shear stress component parameter sequence.

[0039] By constructing time series for each type of geological parameter along the excavation steps and calculating the mean square value and second derivative of the series, the uncertainty of the parameters and the precursors of instability are transformed from qualitative experience into objective statistical indicators. Parameters with the largest mean square value are identified as floating data, reflecting drastic spatial variations or measurement fluctuations in the surrounding rock properties; parameters with the largest absolute value of the second derivative are identified as unstable data, marking the inflection point where the parameter is about to enter accelerated deterioration. This automated screening allows subsequent sensitivity analysis to focus on the few key parameters that are most dominant and dangerous to deformation, avoiding computational redundancy and ambiguity of physical meaning caused by blind perturbation of all parameters.

[0040] Step 5: Adjust the geological data according to the data range in the floating data and the second derivative value in the unstable data to obtain several geological data sets. Repeat step 3 for each geological data set to obtain several predicted second displacement fields and output them.

[0041] Step 5 includes the following: Step 501: Obtain the fluctuation range of the data within the floating sequence, and calculate its data limit based on the second derivative value of the unstable data. The calculation logic is as follows: Using the current excavation step value as a known point, the limit data is obtained twice based on the second-order differential value; Divide the numerical range within the floating range into three equal parts, and combine the upper and lower limits of the floating range to form a total of four data points.

[0042] Four representative values ​​with uniform distribution are constructed from the actual range of fluctuation in the floating data through trisection interpolation. Simultaneously, the limiting value is obtained by extrapolating twice along the current trend based on the second derivative of the unstable data. This captures both normal fluctuations and the most unfavorable accelerated deterioration scenario within the possible deviation space of the parameters. This deterministic scenario generation method requires no random sampling, systematically covers the variation range of the floating parameters with only a few combinations, and quantifies the risk of asymptotic instability into clear data boundaries, providing a structured blueprint for parameter perturbation prediction across multiple scenarios.

[0043] Step 502: Adjust the floating and unstable data in the current excavation step respectively, and obtain four geological data sets. The adjustment logic is as follows: During the actual excavation, the four data points formed by the floating range are replaced with the parameter values ​​corresponding to the geological data used in the simulation inversion, and the replacement is carried out four times in total to form four adjusted geological data. Then, the limit data of the instability data is replaced with the corresponding parameter values ​​in these four adjusted geological data. In a preferred embodiment, when the density parameter sequence is floating data, the range of density is determined, and each time it is adjusted, the density data in the geological data is replaced with one of the four data points to form a new geological data set. When the tensile strength parameter sequence is unstable data, the tensile strength in the geological data is changed to the limit data, and a new geological data set is formed.

[0044] The four floating parameter interpolation points replace the corresponding items in the original geological profile, and the instability parameter limit values ​​simultaneously replace the corresponding items in all adjusted sets, generating four internally consistent composite geological data sets, each containing the most unfavorable instability factors. Each replacement represents a reasonable construction geological assumption that superimposes parameter fluctuation scenarios and extreme deterioration, expanding the single deterministic geological input into a scenario set that systematically covers the main risk dimensions. This enables subsequent displacement prediction to be upgraded from single-value estimation to interval estimation and extreme trend assessment, providing a differentiated input basis for evaluating tunnel safety under changes in rock mass properties.

[0045] Step 503: Simulate and invert the four geological data sets respectively, input them into the first judgment model, obtain four predicted first displacement components and predicted first strain, and input the four first components into the second judgment model respectively to obtain four predicted second displacement fields; The four predicted second displacement fields and the current second displacement field are output respectively.

[0046] The four scenario geological data sets are sequentially processed through the same complete pipeline: "simulation inversion → physical calculation of the first judgment model → temporal recursion of the second judgment model," outputting four sets of predicted future displacement fields in parallel, which are presented alongside the unperturbed baseline predicted displacement. This isomorphic processing path ensures strict comparability between the displacements of each scenario. The degree of dispersion directly quantifies the propagation amplitude and direction of geological parameter uncertainties to tunnel deformation response, intuitively revealing which parameter perturbations may trigger displacement exceedances. This transforms the invisible risk of rock mass variation into measurable and comparable displacement envelopes and worst-case deformation warnings, providing a risk-oriented, multi-dimensional decision-making basis for adjusting support schemes and construction steps at the construction site.

[0047] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0048] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0049] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0050] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A dynamic prediction method for tunnel displacement field based on physical information neural network, characterized in that, The specific steps include: Step 1: Obtain the original dataset through the historical excavation process. The original dataset includes tunnel displacement field, stress-strain field and geological data. Input the original data into simulation software for simulation inversion to obtain time series displacement field and strain field data. Step 2: Using the geological data corresponding to each excavation step as the first sample and the corresponding displacement field and strain field data as labels, train in the PINN model to obtain the first judgment model. Using the time series displacement field and strain field data as the second sample and the corresponding displacement field data as samples, train in the P-LSTM model to obtain the second judgment model. Step 3: Obtain the original dataset of the actual excavation process, perform simulation inversion using the geological data in it, and use the inversion results to obtain the current first displacement component and the current first strain variable in the first judgment model. Combine the current first displacement component and the current first strain variable with the tunnel displacement field and stress-strain field and input them into the second judgment model to obtain the current second displacement field of the next excavation step. Step 4: Based on the time sequence of each parameter type in the geological data of each excavation step in the actual excavation process, form a parameter sequence, and select floating data and unstable data according to the numerical changes in each parameter sequence; Step 5: Adjust the geological data according to the data range in the floating data and the second derivative value in the unstable data to obtain several geological data sets. Repeat step 3 for each geological data set to obtain several predicted second displacement fields and output them.

2. The dynamic prediction method for tunnel displacement field based on physical information neural network according to claim 1, characterized in that: The original dataset is obtained through historical tunnel excavation processes. This dataset includes the tunnel displacement field, stress-strain field, and corresponding timestamps and geological data at various locations during each excavation. This data is then input into numerical simulation software for dynamic simulation and inversion. The geological data includes elastic modulus, Poisson's ratio, cohesion, internal friction angle, tensile strength, density, initial ground stress components, and shear stress components. The geological data required for the dynamic simulation is obtained by setting time windows, the length of which is the duration of several excavation steps. Displacement and strain field data within each time window are obtained through the simulation process. These displacement and strain field data are time-stamped data sequences; the displacement field data represents displacement components, and the strain field data represents strain variables.

3. The dynamic prediction method for tunnel displacement field based on physical information neural network according to claim 2, characterized in that: The geological data of each excavation step in the simulation inversion process is read to form the first sample. The displacement component and strain corresponding to the excavation step are used as labels and input into the PINN model for training. The trained model is labeled as the first judgment model and the output is the first displacement component and the first strain of the excavation step.

4. The dynamic prediction method for tunnel displacement field based on physical information neural network according to claim 3, characterized in that: Several consecutive displacement and strain field data are organized into a second sample, and the first displacement field data after this sample is used as the label. The sample is then input into the P-LSTM model for training. The trained model is labeled as the tunnel displacement field model, and the output is the second displacement field after this excavation step. The trained model is labeled as the second judgment model.

5. The dynamic prediction method for tunnel displacement field based on physical information neural network according to claim 4, characterized in that: In the actual excavation process, the tunnel displacement field and stress-strain field of each excavation step are recorded in chronological order. The actual displacement field and strain field data are simulated and input into the first judgment model to obtain the current first displacement component and the current first strain. Input the current first displacement component and the current first strain as the current displacement field and strain field data into the second judgment model to obtain the current second displacement field after this excavation step.

6. The dynamic prediction method for tunnel displacement field based on physical information neural network according to claim 5, characterized in that: All geological data during each excavation step are acquired, and corresponding parameter sequences are formed according to the data type and acquisition time order. The mean square value and second derivative value within each parameter sequence are obtained. The second derivative value is the last second derivative value calculated with the latest geological data. The parameter sequence with the largest mean square value is identified and labeled as floating data, and the parameter sequence with the largest absolute value of the second derivative value is identified and labeled as unstable data.

7. The dynamic prediction method for tunnel displacement field based on physical information neural network according to claim 6, characterized in that: The fluctuation range of the data within the floating sequence is obtained, and its data limit is calculated based on the second derivative value of the unstable data. The calculation logic is as follows: Using the current excavation step value as a known point, the limit data is obtained twice based on the second-order differential value; Divide the numerical range within the floating range into three equal parts, and combine the upper and lower limits of the floating range to form a total of four data points.

8. The dynamic prediction method for tunnel displacement field based on physical information neural network according to claim 7, characterized in that: Adjust the floating and unstable data in the current excavation step separately to obtain four geological data sets. The adjustment logic is as follows: During the actual excavation, the four data points formed by the floating range are used to replace the parameter values ​​of the geological data used in the simulation inversion. This process is repeated four times to form four adjusted geological data. Then, the limit data of the instability data is used to replace the corresponding parameter values ​​in these four adjusted geological data.

9. The dynamic prediction method for tunnel displacement field based on physical information neural network according to claim 8, characterized in that: The four geological datasets are simulated and inverted respectively, and then input into the first judgment model to obtain four predicted first displacement components and predicted first strain. The four first components are then input into the second judgment model to obtain four predicted second displacement fields. The four predicted second displacement fields and the current second displacement field are output respectively.

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