Beidou high-precision ground deformation monitoring method based on physical constraints and lstm

Abstract

The application discloses a Beidou high-precision ground surface deformation monitoring method based on physical constraints and LSTM, and relates to the technical fields of Beidou high-precision positioning and physical information deep learning. In view of the problems that the existing ground surface deformation monitoring method has insufficient modeling capacity for strong nonlinear deformation, a pure data-driven model is prone to overfitting, and the model has poor physical interpretability, the method first acquires a Beidou three-dimensional coordinate time sequence and a spatial geology parameter set, constructs a vertical consolidation constraint field containing three components of primary consolidation, secondary consolidation and creep, and simultaneously generates a periodic deformation prior based on harmonic fitting; then through a long short-term memory network embedded with double physical constraints, a triple weighted loss framework of data fitting, periodic constraint and consolidation constraint is used for joint training, and a refined three-dimensional ground surface deformation sequence is output. The application significantly improves the deformation calculation precision, suppresses overfitting in a data sparse scene, enhances the physical reliability of the model, and is suitable for high-precision ground surface deformation monitoring in soft soil development areas.

Description

Technical Field

[0001] This invention relates to the fields of BeiDou high-precision positioning and physical information deep learning technology, and in particular to a BeiDou high-precision surface deformation monitoring method based on physical constraints and LSTM. Background Technology

[0002] Surface deformation monitoring is a core technological support for geological disaster early warning, urban safety operation and maintenance, and deformation control of major engineering projects. Currently, high-precision deformation monitoring using BeiDou / GNSS generally employs a technical approach combining baseline calculation with Kalman filter adjustment, relying on software such as GAMIT / GLOBK to obtain coordinate time series and deformation rates. This method, based on the linear Gaussian state-space assumption, struggles to accurately capture the exponential decay and logarithmic growth composite nonlinear deformation patterns and long-term dependencies when dealing with the strongly nonlinear consolidation deformation of soft soil foundations. The accuracy of vertical deformation calculation is limited, failing to fully meet the high-precision monitoring requirements under complex working conditions.

[0003] With the development of deep learning technology, time-series models such as Long Short-Term Memory (LSTM) networks have been used for deformation sequence fitting. However, the purely data-driven training mode is highly dependent on the amount of observation data, and is prone to overfitting in scenarios with sparse monitoring data and complex noise. Furthermore, the models lack physical meaning, making it difficult to guarantee the reliability of the results. Existing physical information neural networks are mostly constrained by partial differential equations and their applications are concentrated in the fields of fluid and solid mechanics. There is currently no solution that simultaneously embeds the three-component soil consolidation analytical model and the harmonic periodic deformation model into the time-series network training. This makes it impossible to achieve quantitative transfer of physical priors from geotechnical tests to deep learning models, thus restricting further improvement in the accuracy of surface deformation monitoring. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a high-precision BeiDou surface deformation monitoring method based on physical constraints and LSTM. This method solves the problems of insufficient modeling capability of traditional Kalman filtering methods for strongly nonlinear surface deformation, and the tendency of pure data-driven deep learning models to overfit and have poor physical interpretability in data-sparse scenarios. It achieves simultaneous improvement in the accuracy, robustness and physical reliability of BeiDou deformation monitoring.

[0005] To achieve the above objectives, this invention provides a BeiDou high-precision surface deformation monitoring method based on physical constraints and LSTM, comprising the following steps: S1. Based on the original BeiDou observation data and the basic engineering geological data of the monitoring area, the BeiDou three-dimensional coordinate time series and spatial geological parameter set are obtained through coordinate frame unification, time reference alignment and deformation symbol standardization. S2. Based on the spatial geological parameter set and the soil consolidation deformation law, the vertical consolidation constraint field is obtained by three-component consolidation settlement modeling and calculation. S3. Based on the periodic deformation characteristics of the BeiDou three-dimensional coordinate time series, the periodic deformation prior is obtained through harmonic fitting and projection operator construction. S4. Based on the BeiDou three-dimensional coordinate time series, vertical consolidation constraint field and periodic deformation prior, a multi-loss joint training optimization is performed by embedding a long short-term memory network with dual physical constraints to obtain a refined three-dimensional surface deformation sequence.

[0006] The advantages and beneficial effects of this invention compared to the prior art are: 1. It can effectively improve the calculation accuracy of BeiDou surface deformation. Through the joint optimization of data fitting loss and two types of physical constraint loss, it can reduce the interference of heterogeneous noise and observation disturbance on deformation calculation results, output a three-dimensional deformation sequence that is more in line with the real deformation evolution law, and ensure the accuracy and reliability of monitoring results.

[0007] 2. This invention has a stronger ability to model complex nonlinear deformation. Relying on the advantages of long short-term memory networks in capturing long-term time-series dependencies, and combined with the physical laws of soil consolidation deformation, it can accurately characterize the nonlinear deformation characteristics of multiple superimposed stages of primary consolidation attenuation, secondary consolidation growth and creep continuous evolution, and adapt to the deformation change laws of different consolidation stages.

[0008] 3. It can significantly improve the robustness of the model in scenarios with sparse data and complex noise. Consolidation constraints and periodic constraints are embedded as structured regularization terms throughout the network training process. They can constrain the fitting direction of the model under conditions of missing observation data and uneven noise distribution, effectively suppress the overfitting problem that is prone to occur in pure data-driven models, and reduce the dependence of the monitoring scheme on the amount and quality of observation data.

[0009] 4. Effectively enhances the physical interpretability of deep learning monitoring models. The deformation sequence output by the network follows both the soil consolidation and settlement mechanism and the seasonal periodic deformation law, breaking through the "black box" limitation of pure data-driven models. This enables the deformation monitoring results to have clear physical causes, facilitating subsequent deformation mechanism analysis and long-term trend judgment.

[0010] 5. It enables efficient knowledge transfer from physical experiments and engineering geological results. Soil consolidation parameters obtained from geotechnical centrifuge tests and engineering geological surveys can be directly converted into constraint boundaries for network training. Existing physical research results can be quantitatively integrated into the deep learning modeling process, improving the efficiency of prior knowledge utilization and the engineering adaptability of the model.

[0011] 6. To ensure the training stability and controllability of physically constrained deep learning networks, both periodic constraints and consolidation constraints use explicit fixed linear operators that can be determined before training to achieve gradient propagation. The gradient propagation path is clear and traceable, avoiding training oscillations, gradient vanishing or gradient explosion problems that are easily caused by implicit physical constraints, thus improving the convergence efficiency and result stability of model training.

[0012] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0013] Figure 1 This is a flowchart of the BeiDou high-precision surface deformation monitoring method based on physical constraints and LSTM in an embodiment of the present invention; Figure 2 This is a schematic diagram of the triple loss physical constraint LSTM training structure according to an embodiment of the present invention. Detailed Implementation

[0014] In the description of this invention, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product is in use. They are used only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. In the description of this invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," and "connect" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0015] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0016] like Figures 1-2 As shown, this invention provides a BeiDou high-precision surface deformation monitoring method based on physical constraints and LSTM, comprising the following steps: S1. Based on the original BeiDou observation data and the basic engineering geological data of the monitoring area, the BeiDou three-dimensional coordinate time series and spatial geological parameter set are obtained through coordinate frame unification, time reference alignment and deformation symbol standardization. S2. Based on the spatial geological parameter set and the soil consolidation deformation law, the vertical consolidation constraint field is obtained by three-component consolidation settlement modeling and calculation. S3. Based on the periodic deformation characteristics of the BeiDou three-dimensional coordinate time series, the periodic deformation prior is obtained through harmonic fitting and projection operator construction. S4. Based on the BeiDou three-dimensional coordinate time series, vertical consolidation constraint field and periodic deformation prior, a multi-loss joint training optimization is performed by embedding a long short-term memory network with dual physical constraints to obtain a refined three-dimensional surface deformation sequence.

[0017] In this embodiment, the BeiDou high-precision surface deformation monitoring method based on physical constraints and LSTM is implemented sequentially according to the process of data preprocessing, consolidation prior construction, periodic prior construction, and multi-constraint network training. This method uses BeiDou observation data with a unified benchmark as input and two types of structured physical priors as training constraints. Deformation sequence refinement is achieved through the synergistic optimization of data-driven and physical constraints. Specifically, data preprocessing eliminates differences in coordinate, time, and symbol benchmarks among multi-source data; dual physical priors provide clear physical guidance for network training; and multi-loss joint training constrains the model output to conform to the physical mechanism of deformation while fitting the observation data.

[0018] Preferably, S1 specifically includes: Based on the original BeiDou observation data, a single-day solution form of the BeiDou three-dimensional coordinate time series was obtained through baseline calculation and Kalman filter adjustment. Based on the cofferdam phase data, stratigraphic exploration parameters and geotechnical test results of the monitoring area, a spatial geological parameter set including the time of completion of hydraulic filling, soil layer thickness, compressibility parameters and permeability parameters was obtained through spatial partitioning and parameter standardization.

[0019] In this embodiment, S1 employs two parallel processing methods: BeiDou data processing and geological parameter organization, to output time-series observation data and spatial attribute parameters, respectively. The BeiDou three-dimensional coordinate time series is obtained through baseline calculation and network adjustment. Baseline calculation refers to calculating the relative position vectors between stations using a double-difference observation model, while network adjustment involves performing an overall adjustment of multi-period baseline results using Kalman filtering to obtain a single-day coordinate sequence under a unified reference framework. The spatial geological parameter set is obtained by organizing engineering survey and cofferdam data, providing spatial dimension parameter support for subsequent physical prior construction.

[0020] Preferably, S2 specifically includes: Based on the dredging completion time corresponding to each spatial location, the vertical consolidation constraint field Scon containing three components is obtained by superimposing the primary consolidation exponential decay model, the secondary consolidation logarithmic growth model and the creep linear model. The formula for calculating the vertically consolidated constraint field is: ; in, The main consolidation settlement component, This is the secondary consolidation settlement component. This is the creep settlement component; The principal consolidation settlement components satisfy: ; The secondary consolidation settlement component satisfies: ; The creep settlement component satisfies: ; In the formula, This represents the time elapsed since the completion of the reclamation. , , For spatial amplitude parameters, , , For the time parameters of the corresponding components, The transition time between primary consolidation and secondary consolidation.

[0021] In this embodiment, the vertical consolidation constraint field is constructed by superimposing three components: primary consolidation, secondary consolidation, and creep, to characterize the physical laws governing the evolution of soil settlement over time. Primary consolidation corresponds to the process of soil pore drainage and compression, with the settlement rate decreasing exponentially over time and eventually stabilizing at a stable settlement amount. Secondary consolidation corresponds to the process of slow adjustment of soil particle positions, with the settlement amount increasing logarithmically over time, typically becoming more prominent after the primary consolidation rate slows down. Creep corresponds to the process of long-term, slow deformation of the soil, with the settlement amount increasing approximately linearly over time. The time elapsed since the completion of the reclamation is the current moment. Each time parameter is used to control the evolution rate of the corresponding deformation process, and the spatial amplitude parameter is used to characterize the total settlement magnitude of the corresponding process.

[0022] Preferably, the determination of the spatial amplitude parameter and the time parameter specifically includes: Based on at least one of the following: geotechnical centrifuge test results, engineering geological survey parameters, and measured settlement sequences, the initial values ​​and ranges of consolidation constraint parameters at each spatial location are obtained through settlement curve fitting and parameter inversion calculation; based on cofferdam zoning, soil layer thickness, compressibility parameters, and permeability parameters, the spatial variation boundaries of the parameters are obtained through spatial correlation constraint processing.

[0023] In this embodiment, the relevant parameters of the consolidation constraint are determined through joint calibration using multi-source data to ensure the physical authenticity and spatial adaptability of the constraint field. Geotechnical centrifuge test results and engineering geological survey parameters can be used to determine the reasonable range and initial values ​​of the parameters, while measured settlement sequences can be used for further fitting and calibration of the parameters. By combining spatial attributes such as cofferdam zoning and soil layer thickness to set spatial variation boundaries for the parameters, the spatial distribution of the constraint field can match the spatial differences in regional geological conditions, preventing parameter values ​​from deviating from the actual geological background.

[0024] Preferably, S3 specifically includes: Harmonic design matrices are constructed based on sine and cosine basis functions with annual and semi-annual cycles. Fixed harmonic projection operators are then constructed using weighted least squares operations. Based on deformation sequences observed by BeiDou, projection calculations are performed using the fixed harmonic projection operators to obtain periodic deformation priors. The calculation formula for the fixed harmonic projection operators is as follows: ; In the formula, Design matrices for harmonic basis functions. To observe the mass weighting matrix, To prevent ill-conditioned matrices, regularization coefficients are used, where I is the identity matrix.

[0025] In this embodiment, the periodic deformation prior is obtained by projecting the observation sequence using a fixed harmonic projection operator, which is used to characterize the seasonal periodic variation of surface deformation. The harmonic design matrix consists of sine and cosine basis functions with annual and semi-annual cycles, corresponding to the annual and semi-annual periodic components that are commonly found in surface deformation. The fixed harmonic projection operator is constructed based on the weighted least squares principle, where the weight matrix is ​​used to characterize the quality differences of different observation data, and the regularization coefficient is used to avoid computational instability caused by ill-conditioned matrices. This operator can be determined based on the observation time before training and remains fixed during training; therefore, it is called the fixed harmonic projection operator, which can achieve explicit gradient propagation.

[0026] Preferably, in S4, the temporal processing of the Long Short-Term Memory network specifically includes: Based on a fixed-length BeiDou three-dimensional coordinate time series window, time-series feature extraction and mapping calculation are performed through a stacked long short-term memory network of 1 to 3 layers to obtain a time-by-time three-dimensional deformation prediction sequence; the three-dimensional deformation prediction sequence includes three components: northward, eastward and vertical.

[0027] In this embodiment, the Long Short-Term Memory (LSTM) network uses a fixed-length time series window as the input unit and achieves layer-by-layer extraction and mapping of temporal features through stacked network layers. The LTM network has a gating structure, which can effectively capture dependencies in long-term time series data and adapt to the long-term evolution characteristics of surface deformation. The sliding window input method allows for segmented processing of long-term time series, and the network outputs the three-dimensional deformation prediction results for each time point within the corresponding window, including three coordinate components: north, east, and vertical. The vertical component is the primary target of consolidation constraints.

[0028] Preferably, in S4, the total loss function optimized by multi-loss joint training specifically includes: Based on BeiDou observation data, periodic deformation priors, and a vertical consolidation constraint field, the total loss function used for network backpropagation updates is obtained through a weighted combination of data fitting loss, periodic constraint loss, and consolidation constraint loss. The formula for calculating the total loss function is as follows: ; In the formula, For BeiDou data fitting loss, For periodic constraint loss, For consolidation constraint loss, For periodic constraint weighting coefficients, This represents the consolidation constraint weighting coefficient.

[0029] In this implementation, a triple-weighted loss function is used as the optimization objective for network training, and the weight parameters of the network are updated through the backpropagation algorithm. The data fitting loss is used to constrain the network output to fit the actual observation data, ensuring the observational consistency of the results; the periodic constraint loss is used to constrain the periodic components of the network output to match the prior periodic law, suppressing the interference of noise on the periodic term; the consolidation constraint loss is used to constrain the vertical trend of the network output to conform to the soil consolidation and settlement mechanism; the three types of losses are weighted and combined through weight coefficients, and the intensity of different constraints can be adjusted according to the application scenario to achieve a balance between data fitting and physical constraints.

[0030] Preferably, the calculation of the three types of loss terms specifically includes: Based on the covariance matrix calculated using BeiDou coordinates, the BeiDou data fitting loss is obtained by calculating the weighted sum of squares of the residuals between the three-dimensional deformation prediction sequence and the observation sequence. Based on the fixed harmonic projection operator, the periodic constraint loss is obtained by extracting the periodic components of the three-dimensional deformation prediction sequence and calculating the sum of squares of the residuals with the periodic deformation prior. Based on the fixed low-pass smoothing operator, the consolidation constraint loss is obtained by extracting the vertical trend components of the three-dimensional deformation prediction sequence and calculating the sum of squares of the residuals with the vertical consolidation constraint field.

[0031] In this embodiment, the three types of loss terms are calculated based on their corresponding physical mechanisms and operators, and each loss term has a clear physical meaning and calculation path. The data fitting loss is weighted based on the covariance matrix calculated by BeiDou, with higher-precision observations having larger weights to avoid low-quality observations excessively affecting the fitting results; the period constraint loss extracts the periodic component of the predicted sequence through a fixed harmonic projection operator and calculates the residual with the prior periodic value; the consolidation constraint loss extracts the vertical trend component of the predicted sequence through a fixed low-pass smoothing operator and calculates the residual with the vertical consolidation constraint field; since the vertical coordinate is positive upwards and the consolidation settlement is positive downwards, the consolidation constraint field is negatively valued before residual matching is performed.

[0032] Preferably, the gradient transfer of the fixed harmonic projection operator and the fixed low-pass smoothing operator specifically includes: Based on the observation time and operator parameters determined before training, the gradient of the physical constraint term is transferred to the network output through explicit linear operation, so that the periodic constraint gradient and the consolidation constraint gradient can work together with the data fitting gradient to update the network weights during backpropagation.

[0033] In this implementation, both types of physical constraints utilize explicit fixed linear operators to propagate gradients, ensuring the stability and interpretability of the backpropagation process. Explicit fixed linear operators refer to linear operation structures whose operator parameters are entirely determined by the observation time and prior parameters before training and remain unchanged during training. Compared to implicit differential equation constraints, the gradient propagation path of this type of operator is fixed and analytically derivable, preventing gradient vanishing or exploding issues. During backpropagation, the periodic constraint gradient and the fixed constraint gradient can be propagated to the network output layer through their respective operators, then superimposed with the data fitting gradient to update the network weights, achieving collaborative optimization across multiple constraints.

[0034] Preferably, the setting of the periodic constraint weight coefficient and the consolidation constraint weight coefficient specifically includes: Based on the duration of the monitoring point distance and the quality of the observation data, the weight coefficients that match the current consolidation stage and data conditions are obtained through validation set optimization or phased adaptive adjustment. The weight coefficients of consolidation constraints are increased in the early consolidation stage after the completion of the dredging and decreased in the later consolidation stage.

[0035] In this embodiment, the constraint weight coefficients can be adaptively adjusted according to the consolidation stage and data conditions to adapt to the constraint requirements under different scenarios. In the early consolidation stage after dredging and filling, the soil settlement law is dominated by consolidation. At this time, increasing the consolidation constraint weight can strengthen the guiding role of physical laws and suppress the interference of data noise. In the later consolidation stage, the consolidation rate slows down and the deformation influencing factors become more complex. At this time, reducing the consolidation constraint weight can improve the adaptability of data-driven approaches. The weight coefficients can also be determined through optimization on the validation set, adjusting the weight values ​​with the goal of achieving the optimal comprehensive accuracy on the validation dataset.

[0036] The following description uses a specific embodiment as an example.

[0037] This embodiment uses BeiDou continuous monitoring stations deployed in reclaimed land areas as the implementation object. The monitoring data spans from October 2020 to October 2025. Combining regional cofferdam phase data, engineering geological survey parameters, and geotechnical centrifuge test results, the following steps are taken to achieve high-precision BeiDou surface deformation monitoring: Step 1: Data acquisition and spatiotemporal unification.

[0038] Raw BeiDou observation data was acquired, and a three-dimensional coordinate time series under a unified reference frame was generated through baseline calculation and network adjustment. Simultaneously, data on cofferdam boundaries, completion times of dredging in each zone, stratum thickness parameters, soil compressibility parameters, and permeability parameters were collected for the monitoring area. Coordinate frame alignment, time reference unification, and deformation sign standardization were performed on all multi-source data to establish a one-to-one correspondence between spatial location and geological parameters, providing standardized input for subsequent physical prior construction and network training.

[0039] Step 2: Consolidation physics prior construction.

[0040] make Where t0(x,y) is the time of completion of dredging at the corresponding spatial location. The cumulative consolidation settlement consists of the superposition of the primary consolidation component, the secondary consolidation component, and the creep component. The vertical consolidation constraint field Scon satisfies: ; The expression for the principal consolidation settlement component is as follows: ; This characterizes the pattern that the cumulative primary consolidation settlement gradually stabilizes over time, while the settlement rate continuously decreases over time.

[0041] The expression for the secondary consolidation settlement component is: In the formula The transition time between primary and secondary consolidation, i.e., the time point at which secondary consolidation begins to manifest; when not using a piecewise model, it can be set as follows: .

[0042] The expression for the creep settlement component is: ; In the above formulas, , , All are spatial amplitude parameters. , , The time parameters are the corresponding components. Based on the results of geotechnical centrifuge tests and engineering geological data, the range and initial values ​​of the above parameters are given. Further fitting and calibration of the parameters can be completed by combining the measured settlement sequence. The completion time of dredging and filling in different cofferdam zones determines the consolidation start time of the corresponding area. Soil permeability, soil thickness and compressibility parameters are used to constrain the spatial variation range of time parameters and spatial amplitude parameters.

[0043] Step 3: Periodic prior construction.

[0044] Harmonic fitting with annual and semi-annual cycles was performed on the deformation sequence of the area covered by BeiDou monitoring stations. ,in To define the harmonic basis function design matrix for a year, its column vectors are as follows: with cos(2) Based on the design matrix, a fixed harmonic projection operator \(H_m\) is constructed, with the expression: ; Periodic deformation prior ,in To observe the deformation sequence. Due to the fixed harmonic projection operator Since the observation time is predetermined before training, and the fixed linear operator is maintained throughout the training process, the gradient can be explicitly transmitted to the output of the long short-term memory network.

[0045] Step 4: Physically constrained LSTM refinement.

[0046] A BeiDou 3D coordinate time series window of length T is selected as the input to the Long Short-Term Memory (LSTM) network. The network adopts a stacked structure of 1 to 3 layers, with the hidden layer dimension set to 64 to 256. The network outputs a time-by-time 3D deformation prediction sequence. For the m-th satellite orbital direction, the 3D prediction sequence is projected onto the line of sight to obtain the LOS direction prediction value: ; In the formula This is the unit vector representing the line of sight to the corresponding satellite.

[0047] The periodic component of the LOS prediction sequence is extracted using a fixed harmonic projection operator, and the trend component of the vertical prediction sequence is extracted using a fixed low-pass matrix G, a fixed spline smoothing matrix, or other differentiable linear trend operators. Three types of loss functions are constructed accordingly: Data fitting loss : ; In the formula The covariance matrix calculated for BeiDou coordinates. To measure the BeiDou coordinate sequence, The number of valid observation samples.

[0048] Periodic constraint loss : ; In the formula For observation mask or quality weight, The number of samples is constrained by the effective period.

[0049] Consolidation constraint loss: ; In the formula The mass weight of the consolidation constraint. This represents the number of samples for effective consolidation; since the vertical coordinate U is positive upwards, the consolidation settlement... The downward direction is positive, so the plus sign is used in the formula to achieve residual matching.

[0050] The total loss function for network training is a weighted combination of the three types of losses: ; In the formula For periodic constraint weighting coefficients, The consolidation constraint weights are determined through optimization on the validation set. When a phased constraint strategy is adopted, a larger weight is set in the early consolidation stage of \(\Deltat\let_c\). This strengthens the constraint effect of the consolidation law; it reduces the later consolidation stage of \(\Deltat>t_c\). This improves the model's data adaptability. The total loss is updated through backpropagation to update the network weights. After completing multi-constraint joint training, a refined 3D surface deformation sequence is output.

[0051] In this application, unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. In case of any inconsistency, the meaning set forth in this specification or derived from the content described herein shall prevail. Furthermore, the terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit the scope of this application.

[0052] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A high-precision BeiDou surface deformation monitoring method based on physical constraints and LSTM, characterized in that, Includes the following steps: S1. Based on the original BeiDou observation data and the basic engineering geological data of the monitoring area, the BeiDou three-dimensional coordinate time series and spatial geological parameter set are obtained through coordinate frame unification, time reference alignment and deformation symbol standardization. S2. Based on the spatial geological parameter set and the soil consolidation deformation law, the vertical consolidation constraint field is obtained by three-component consolidation settlement modeling and calculation. S3. Based on the periodic deformation characteristics of the BeiDou three-dimensional coordinate time series, the periodic deformation prior is obtained through harmonic fitting and projection operator construction. S4. Based on the BeiDou three-dimensional coordinate time series, vertical consolidation constraint field and periodic deformation prior, a multi-loss joint training optimization is performed by embedding a long short-term memory network with dual physical constraints to obtain a refined three-dimensional surface deformation sequence.

2. The BeiDou high-precision surface deformation monitoring method based on physical constraints and LSTM according to claim 1, characterized in that, S1 specifically includes: Based on the original BeiDou observation data, a single-day solution form of the BeiDou three-dimensional coordinate time series was obtained through baseline calculation and Kalman filter adjustment. Based on the cofferdam phase data, stratigraphic exploration parameters and geotechnical test results of the monitoring area, a spatial geological parameter set including the time of completion of hydraulic filling, soil layer thickness, compressibility parameters and permeability parameters was obtained through spatial partitioning and parameter standardization.

3. The BeiDou high-precision surface deformation monitoring method based on physical constraints and LSTM according to claim 1, characterized in that, S2 specifically includes: Based on the dredging completion time corresponding to each spatial location, the vertical consolidation constraint field Scon containing three components is obtained by superimposing the primary consolidation exponential decay model, the secondary consolidation logarithmic growth model and the creep linear model. The formula for calculating the vertical consolidation constraint field is as follows: ; in, The main consolidation settlement component, This is the secondary consolidation settlement component. This is the creep settlement component; The principal consolidation settlement components satisfy: ; The secondary consolidation settlement component satisfies: ; The creep settlement component satisfies: ; In the formula, This represents the time elapsed since the completion of the reclamation. , , For spatial amplitude parameters, , , For the time parameters of the corresponding components, The transition time between primary consolidation and secondary consolidation.

4. The BeiDou high-precision surface deformation monitoring method based on physical constraints and LSTM according to claim 3, characterized in that, The determination of the spatial amplitude parameters and time parameters specifically includes: Based on at least one of the following: geotechnical centrifuge test results, engineering geological survey parameters, and measured settlement sequences, the initial values ​​and ranges of consolidation constraint parameters at each spatial location are obtained through settlement curve fitting and parameter inversion calculation; based on cofferdam zoning, soil layer thickness, compressibility parameters, and permeability parameters, the spatial variation boundaries of the parameters are obtained through spatial correlation constraint processing.

5. The BeiDou high-precision surface deformation monitoring method based on physical constraints and LSTM according to claim 4, characterized in that, S3 specifically includes: Harmonic design matrices are constructed based on sine and cosine basis functions with annual and semi-annual cycles. A fixed harmonic projection operator is then constructed using weighted least squares operations. Based on deformation sequences observed via BeiDou, projection calculations are performed using the fixed harmonic projection operator to obtain periodic deformation priors. The calculation formula for the fixed harmonic projection operator is as follows: ； In the formula, Design matrices for harmonic basis functions. To observe the mass weighting matrix, To prevent ill-conditioned matrices, regularization coefficients are used, where I is the identity matrix.

6. The BeiDou high-precision surface deformation monitoring method based on physical constraints and LSTM according to claim 5, characterized in that, In step S4, the temporal processing of the Long Short-Term Memory network specifically includes: Based on a fixed-length BeiDou three-dimensional coordinate time series window, time-series feature extraction and mapping calculation are performed through a stacked long short-term memory network of 1 to 3 layers to obtain a time-by-time three-dimensional deformation prediction sequence; the three-dimensional deformation prediction sequence includes three components: northward, eastward and vertical.

7. The BeiDou high-precision surface deformation monitoring method based on physical constraints and LSTM according to claim 6, characterized in that, In S4, the total loss function for multi-loss joint training optimization specifically includes: Based on BeiDou observation data, periodic deformation priors, and a vertical consolidation constraint field, a total loss function for network backpropagation updates is obtained through a weighted combination of data fitting loss, periodic constraint loss, and consolidation constraint loss. The formula for calculating the total loss function is as follows: ； In the formula, For BeiDou data fitting loss, For periodic constraint loss, For consolidation constraint loss, For periodic constraint weighting coefficients, This represents the consolidation constraint weighting coefficient.

8. The BeiDou high-precision surface deformation monitoring method based on physical constraints and LSTM according to claim 7, characterized in that, The calculation of the three types of loss terms specifically includes: Based on the covariance matrix calculated using BeiDou coordinates, the BeiDou data fitting loss is obtained by calculating the weighted sum of squares of the residuals between the three-dimensional deformation prediction sequence and the observation sequence. Based on the fixed harmonic projection operator, the periodic constraint loss is obtained by extracting the periodic components of the three-dimensional deformation prediction sequence and calculating the sum of squares of the residuals with the periodic deformation prior. Based on the fixed low-pass smoothing operator, the consolidation constraint loss is obtained by extracting the vertical trend components of the three-dimensional deformation prediction sequence and calculating the sum of squares of the residuals with the vertical consolidation constraint field.

9. The BeiDou high-precision surface deformation monitoring method based on physical constraints and LSTM according to claim 8, characterized in that, The gradient transfer of the fixed harmonic projection operator and the fixed low-pass smoothing operator specifically includes: Based on the observation time and operator parameters determined before training, the gradient of the physical constraint term is transferred to the network output through explicit linear operation, so that the periodic constraint gradient and the consolidation constraint gradient can work together with the data fitting gradient to update the network weights during backpropagation.

10. The BeiDou high-precision surface deformation monitoring method based on physical constraints and LSTM according to claim 9, characterized in that, The setting of the periodic constraint weighting coefficient and the consolidation constraint weighting coefficient specifically includes: Based on the duration of the monitoring point distance and the quality of the observation data, the weight coefficients that match the current consolidation stage and data conditions are obtained through validation set optimization or phased adaptive adjustment. The weight coefficients of consolidation constraints are increased in the early consolidation stage after the completion of the dredging and decreased in the later consolidation stage.

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