Ground surface settlement prediction method based on variational mode decomposition and BP neural network
By combining SBAS-InSAR with VMD decomposition and BP neural network to predict land subsidence, the problem of noise interference and nonlinear characteristics is solved, achieving efficient and accurate land subsidence prediction. It is applicable to a variety of subsidence scenarios and provides reliable early warning support.
Patent Information
- Application Number
- CN202511294364.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-11
- Publication Date
- 2025-12-23
AI Technical Summary
Existing technologies for predicting land subsidence suffer from problems such as difficulty in effectively eliminating noise interference, difficulty in accurately capturing nonlinear features, complex model structures, and low computational efficiency, resulting in insufficient prediction accuracy and difficulties in practical applications.
Combining SBAS-InSAR technology with VMD decomposition, a BP neural network is used to model each modal component. Through component prediction superposition and feedback optimization, noise stripping and trend extraction are achieved. The training is efficient and resource consumption is low, making it suitable for various settlement scenarios.
It improves the accuracy and robustness of surface subsidence prediction, is applicable to various subsidence scenarios such as mining areas and cities, provides reliable decision support for geological disaster early warning, and has a simple model structure, fast training, and strong adaptability.
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Figure CN121189152A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of geological disaster monitoring and prediction, and more particularly to a surface subsidence prediction method based on variational mode decomposition and BP neural network. BACKGROUND
[0002] Surface subsidence is a process of surface height reduction caused by natural or human factors, which is common in mining areas, overexploitation of groundwater, compaction of foundations, etc. It has brought serious threats to infrastructure, ecological environment and personnel safety. Traditional surface subsidence monitoring methods, such as leveling and GPS network monitoring, have obvious defects. First, the spatial coverage is limited, making it difficult to fully grasp the subsidence situation in a large area. Second, the cost is high, which is not conducive to large-scale popularization and application. Third, it is easily affected by weather factors, resulting in poor stability and continuity of monitoring work.
[0003] In recent years, InSAR technology has gradually become the mainstream means in the field of surface subsidence monitoring due to its large-scale, high-precision and all-weather monitoring capabilities. Among them, SBAS-InSAR technology can obtain high temporal resolution subsidence time series data, providing solid data support for subsequent surface subsidence prediction.
[0004] However, when using these historical subsidence time series data for prediction, it is easy to be disturbed by noise, non-stationary and nonlinear characteristics in the data by relying solely on trend extrapolation, resulting in insufficient prediction accuracy. To solve this problem, signal processing methods and machine learning methods are introduced in related research. Signal processing methods such as EMD, VMD and SSA can decompose the original time series into multiple components, and then extract different frequency band and trend information. Machine learning methods such as LSTM and BP neural network have strong modeling ability in time series prediction. Existing research often combines VMD with LSTM, or uses VMD-SSA-LSTM combination, but these combined models still have certain limitations in practical application. For example, the LSTM network structure is complex, the training process is time-consuming, and the computing resources required are high. Although the multi-step combined model (such as VMD-SSA-LSTM) may have improved accuracy, the model construction and parameter adjustment process is complicated, and the controllability is poor, which is not conducive to rapid deployment and application in practical engineering. At the same time, although the BP neural network has the advantages of simple structure and fast training speed, the existing technology does not have in-depth application research on its combination with VMD, which fails to fully exploit the potential of the combination of the two in dealing with noise interference, capturing nonlinear characteristics and improving model efficiency and controllability.
[0005] In general, existing technologies for land subsidence prediction suffer from the following problems: First, noise interference is difficult to eliminate effectively, affecting the accuracy of prediction data; second, the nonlinear characteristics of subsidence time series are complex, making it difficult for existing models to accurately model them; and third, some combined models have complex structures, cumbersome training processes, low computational efficiency, and poor controllability, hindering practical application. Therefore, how to provide a land subsidence prediction method that can effectively suppress noise, accurately capture nonlinear characteristics, and simultaneously possess high computational efficiency and model controllability has become an urgent technical problem to be solved. Summary of the Invention
[0006] In view of this, this application provides a surface subsidence prediction method based on variational mode decomposition and BP neural network. It combines SBAS-InSAR and VMD decomposition, and uses BP neural network to model each modal component separately to achieve accurate noise removal and key trend extraction. The method is highly efficient in training and low in resource consumption. The accuracy and robustness are greatly improved by component prediction superposition and feedback optimization. It is easy to replace time series models and is applicable to various subsidence scenarios such as mining areas and cities, providing reliable decision support for geological disaster early warning and prevention.
[0007] The technical solution provided in this application is as follows:
[0008] A method for predicting land subsidence based on variational mode decomposition and BP neural network includes:
[0009] Acquire multi-temporal SAR images of the area to be monitored;
[0010] After performing topographic phase correction and atmospheric delay phase correction on the multi-temporal SAR images, an interferometric pair network is constructed using the small baseline set SBAS technique. After noise removal from the interferogram, screening of low coherence areas, and phase unwrapping, the acquired absolute phase is converted into surface subsidence and geocoded to obtain the spatiotemporal distribution of subsidence in the area to be monitored, so as to extract the original temporal signal of the surface subsidence monitoring point.
[0011] VMD is used to perform multi-scale decomposition on the original time-series signal to obtain multiple intrinsic mode functions (IMFs). The target mode function is selected based on the energy contribution or signal-to-noise ratio of each IMF.
[0012] The historical time series data of the selected target mode functions are used as input to the BP neural network. The BP neural network is trained and future time series predictions are made for each IMF component. The prediction results of each IMF component are superimposed to obtain the overall surface subsidence prediction result.
[0013] The overall surface subsidence prediction results are compared with the actual observation data. If the prediction performance does not meet the preset standard, the VMD decomposition parameters or BP neural network parameters are adjusted and the above steps are repeated until a prediction result that meets the preset standard is obtained.
[0014] In one possible implementation, after obtaining the multi-temporal SAR images of the region to be monitored, the method further includes:
[0015] obtaining digital elevation model (DEM) data, atmospheric correction data, and satellite precise orbit data corresponding to the multi-temporal SAR images; wherein the DEM data is used for terrain phase correction of the multi-temporal SAR images, and the satellite precise orbit data is used for phase deviation caused by satellite orbit position error.
[0016] In one possible implementation, the interferometric pair network is constructed using the small baseline subset (SBAS) technique, including:
[0017] estimating the baseline of the corrected multi-temporal SAR images to determine the spatial baseline and the temporal baseline of the multi-temporal SAR images;
[0018] filtering the multi-temporal SAR images that meet the conditions according to a preset baseline threshold to generate interferometric pairs and form the interferometric pair network; wherein the baseline threshold includes a spatial baseline threshold and a temporal baseline threshold.
[0019] In one possible implementation, after the interferometric pair network is constructed using the SBAS technique, the method further includes:
[0020] selecting a stable area as a reference point in the region to be monitored, wherein the reference point is an area with high coherence and no significant deformation;
[0021] generating an interferogram, removing noise, and unwrapping the phase based on the interferometric pair network to obtain continuous absolute phase;
[0022] extracting the time-series phase change of each monitoring point in the region to be monitored based on the unwrapped absolute phase, converting the time-series phase change into corresponding ground subsidence, and obtaining the spatio-temporal distribution of the region to be monitored after geocoding.
[0023] In one possible implementation, the VMD is used to perform multi-scale decomposition on the time-series original signal to obtain a plurality of intrinsic mode functions (IMFs), including:
[0024] performing multi-scale decomposition on the time-series original signal, and decomposing the time-series original signal into a plurality of IMFs by constructing and solving an optimization objective function; wherein the optimization objective function is used to minimize the bandwidth of each IMF, and the sum of all IMFs is equal to the time-series original signal; the optimization objective function is solved by iteratively updating each IMF and the corresponding center frequency, and is expressed as:
[0025]
[0026] wherein u k (t) is the kth modal function, ω k is the corresponding center frequency, and u k (t) and ω k are updated by iteration, to obtain the decomposed modal function; denotes the partial derivative with respect to time, and δ(t) denotes the Dirac delta function; denotes the square of the L2 norm.
[0027] In one possible implementation, the historical time series data of the target modal function selected is taken as the input of the BP neural network, and the BP neural network is trained, including:
[0028] The training samples are constructed in a sliding window manner, wherein the sample input is a combination of the values of the previous N steps of each of the plurality of IMF components in the historical time series, and the sample label is a combination of the values of the current step or a future step of the plurality of IMF components in the time series.
[0029] In one possible implementation, the overall ground surface settlement prediction result is compared with the actual observation data to determine whether the prediction performance meets the preset standard, including:
[0030] The prediction error RMSE, MAE, and MAPE between the overall ground surface settlement prediction result and the actual observation result is calculated, and the prediction error is compared with the preset standard.
[0031] Based on the comparison result, the VMD parameters or the BP neural network structure and hyperparameters are adjusted, and the decomposition, training, and prediction are performed again, and the above steps are repeated until the prediction error tends to be stable.
[0032] Compared with the prior art, the technical scheme provided in the application has the following beneficial effects:
[0033] With the aid of the SBAS-InSAR technology and auxiliary data processing, the application can accurately obtain the spatiotemporal distribution of the settlement of the region to be monitored, and provide a reliable basis for subsequent analysis. The VMD decomposition and the selection of effective IMF components based on energy contribution and signal-to-noise ratio can effectively strip noise interference, focus on the core settlement characteristics, and improve the signal quality. The prediction of the selected components by the BP neural network and the superposition of the results, combined with the parameter optimization and feedback mechanism, greatly enhance the model's ability to capture complex settlement patterns and prediction accuracy, and can dynamically adapt to different scenarios to ensure stable and reliable prediction results. The application provides strong technical support for ground surface settlement disaster warning and regional planning. BRIEF DESCRIPTION OF DRAWINGS
[0034] Figure 1A flowchart of a ground subsidence prediction method based on variational mode decomposition and BP neural network is provided for the embodiment one of the present application.
[0035] Figure 2 A flowchart of a ground subsidence prediction method based on variational mode decomposition and BP neural network is provided for the embodiment two of the present application.
[0036] Figure 3 A structural schematic diagram of the BP neural network is provided for the embodiment two of the present application.
[0037] Figure 4 A graph of the overall average deformation rate is provided for the embodiment two of the present application.
[0038] Figure 5 A comparison graph of the prediction results of different models is provided for the embodiment two of the present application. DETAILED DESCRIPTION
[0039] The technical solutions in the embodiments of the present application will be described clearly and completely below, obviously, the described embodiments are only part of the embodiments of the present application, not all the embodiments, based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the protection scope of the present application.
[0040] Embodiment one
[0041] Reference Figure 1 A ground subsidence prediction method based on variational mode decomposition and BP neural network is provided for the embodiment one of the present application. As shown in Figure 1 The specific implementation steps of the above method include:
[0042] Step 101, acquiring multi-temporal SAR images of a region to be monitored.
[0043] Step 102, after terrain phase correction and atmospheric delay phase correction on the above multi-temporal SAR images, adopting SBAS technology to construct an interference pair network, after interference graph noise elimination, low-coherence area screening and phase unwrapping, converting the acquired absolute phase into ground subsidence and geocoding, obtaining the subsidence spatio-temporal distribution of the region to be monitored, to extract the time sequence original signal of the ground subsidence monitoring point.
[0044] Step 103, adopting VMD to perform multi-scale decomposition on the above time sequence original signal to obtain a plurality of intrinsic mode functions (IMF), and screening out a target mode function based on the energy contribution degree or signal-to-noise ratio of each IMF.
[0045] Step 104, taking the screened historical time series data of the target modal function as the input of the BP neural network, training the BP neural network and performing future time series prediction on each IMF component, and superimposing the prediction results of each IMF component to obtain the overall ground subsidence prediction result.
[0046] Step 105, comparing the overall ground subsidence prediction result with the actual observation data, if the prediction performance does not reach the preset standard, adjusting the VMD decomposition parameters or the BP neural network parameters and re-executing the foregoing steps until the prediction result meeting the preset standard is obtained.
[0047] Compared with the prior art, the technical scheme provided by the embodiment one of the present application has the following beneficial effects:
[0048] The application discloses a ground subsidence prediction method based on combination of variational mode decomposition (VMD) and BP neural network, which is suitable for high-precision prediction by using subsidence time series data extracted by multi-temporal SBAS-InSAR. First, multi-temporal SAR images of a research area and corresponding DEM, atmospheric correction and precise orbit data are acquired, and the subsidence time series is extracted through the SBAS-InSAR process; then, the subsidence time series is decomposed by VMD, and a BP neural network is constructed and trained for each IMF component, and future time series prediction is performed by taking the historical sequence as the input; finally, the prediction results of each component are superimposed to form the overall ground subsidence prediction, and the prediction results are compared with the actual observation by calculating the RMSE, MAE and MAPE indexes, and the VMD or BP model parameters are adjusted as needed to optimize the performance. The method provided by the application has the advantages of simple structure, efficient training, modeling of different frequency band signals respectively, superposition, improved prediction accuracy and robustness, and significant application value.
[0049] Embodiment two
[0050] Reference Figure 2 A ground subsidence prediction method based on combination of variational mode decomposition (VMD) and BP neural network is provided for the embodiment two of the present application. As shown in Figure 2 The specific implementation steps of the method include:
[0051] Step 201, acquiring multi-temporal SAR images of a region to be detected and corresponding auxiliary data, including but not limited to digital elevation model (Digital Elevation Model; hereinafter referred to as DEM) data, atmospheric correction data and satellite precise orbit data. The satellite precise orbit data is used to eliminate the phase deviation caused by the satellite orbit position error and improve the accuracy of the ground subsidence calculation.
[0052] For example, the atmospheric correction data can be atmospheric delay correction data (Generic Atmospheric Correction Online Service for InSAR; hereinafter referred to as GACOS) or other atmospheric correction data for synthetic aperture radar interferometry (InSAR) data, and embodiments of the present application are not limited in this regard.
[0053] Step 202, pre-processing the multi-temporal SAR image, including terrain phase correction based on the DEM data, and atmospheric delay phase correction based on the atmospheric correction data.
[0054] Step 203, based on the corrected multi-temporal SAR image, constructing an interferometric pair network using the small baseline set (SBAS) technique.
[0055] Among them, the interferometric pairs in the constructed interferometric pair network meet the preset time baseline and spatial baseline threshold to ensure image coherence, and the stable area in the monitoring area is selected as the reference point.
[0056] Step 204, generating an interferogram based on the interferometric pair network, and performing noise removal and low coherence area screening on the interferogram.
[0057] Step 205, phase unwrapping of the screened interferogram to obtain continuous absolute phase.
[0058] Step 206, based on the unwrapped absolute phase, extracting the time series phase change of each monitoring point in the monitoring area, and converting the time series phase change into the corresponding land subsidence, and after geocoding, obtaining the subsidence spatiotemporal distribution of the monitoring area.
[0059] As shown in Figure 4 , the present application takes the spatiotemporal average value of the land subsidence as the overall average deformation rate to reflect the spatial differentiation of the regional subsidence trend.
[0060] Step 207, based on the subsidence spatiotemporal distribution, obtaining the time series original signal of the land subsidence monitoring point.
[0061] Among them, the time series original signal is a sequence of land subsidence changing with time extracted by InSAR technology.
[0062] Step 208, using variational mode decomposition (VMD) to perform multi-scale decomposition on the time series original signal, and by constructing and solving an optimization objective function, the time series original signal is decomposed into multiple IMFs.
[0063] In the embodiments of the present application, the optimization objective function is used to minimize the bandwidth of each IMF and constrain the sum of all IMFs to be equal to the aforementioned time series original signal. The optimization objective function is solved by iteratively updating each IMF and its corresponding center frequency, and is expressed as:
[0064]
[0065] In the formula, u k (t) is the kth modal function, ω k is the center frequency, which is obtained by iteratively updating u k (t) and ω k to obtain the decomposed modal function. The partial derivative with respect to time represents the rate of change of the signal. δ(t) represents the Dirac delta function, i.e., the unit impulse function. The square of the L2 norm is used to quantify the energy of the signal.
[0066] Step 209, based on the energy contribution or signal-to-noise ratio of each IMF, the effective surface subsidence information is reserved by screening out the IMF that has a significant contribution to the prediction of surface subsidence trend.
[0067] Specifically, the energy contribution of a certain IMF refers to the proportion of the energy of the IMF in the total energy of all IMFs. The higher the energy, the greater the proportion of the component in the original signal, and the more important information it contains. The signal-to-noise ratio SNR refers to the ratio of the effective signal to the noise in the IMF. The higher the signal-to-noise ratio, the less the component is affected by noise, and the purer the signal. Through these quantitative indicators, the embodiments of the present application can avoid relying on subjective judgments such as frequency characteristics, making the screening process more objective and repeatable.
[0068] For the target modal function that has a significant contribution to the prediction of the surface subsidence area, as an implementable way, the embodiments of the present application reserve the IMF component with an energy contribution of ≥5% and a signal-to-noise ratio of ≥10dB as the effective component that has a significant contribution to the prediction of the surface subsidence trend. Currently, the aforementioned thresholds can be set according to the actual scene, and the embodiments of the present application are not limited specifically, but it should be noted that any technical solution that sets the thresholds of energy contribution and signal-to-noise ratio respectively to screen the effective component should fall within the aforementioned protection scope of the present application.
[0069] Step 210, combining the historical time series data of the screened IMFs as input to construct a BP neural network.
[0070] Specifically, for each selected IMF component, a BP neural network is constructed. The network structure and training hyperparameters of the BP neural network are determined by cross-validation or automatic search, and early stopping or regularization methods are used in the model training process to prevent overfitting.
[0071] As Figure 3 The BP neural network provided by the embodiments of the present application includes an input layer, a hidden layer and an output layer, as shown in the specification. Training samples are constructed in a sliding window manner. The sample input is a combination of values of the previous N steps of each of the plurality of IMF components in the historical time sequence, and the sample label is a combination of values of the current step or a future step of the plurality of IMF components in the time sequence. The input layer converts the historical N-step values of each of the IMF components into a feature vector that can be received by the BP neural network, and transmits the feature vector to the hidden layer through full connection weights. The initial values and updating method of the full connection weights are determined by training hyperparameters, including learning rate, optimizer, etc. The activation function of the hidden layer introduces nonlinearity in the output of each neuron, enabling the network to fit complex subsidence time series relationships. The output layer is used to output the final prediction value, such as the ground subsidence at a future time.
[0072] In a specific implementation, the BP neural network is initialized, the full connection weights are randomly assigned, the activation function of the hidden layer is in the initial state, and the fitting ability of the network to the subsidence law is close to random. The input IMF time series data is input into the network, the hidden layer performs nonlinear transformation, and the output layer generates a prediction value. The error (such as MSE) is calculated by comparing the true value, the connection weights are adjusted by back propagation, and the extraction ability of the hidden layer to the subsidence features is gradually optimized. After selecting the parameters by cross-validation and controlling overfitting by early stopping / regularization, the input layer of the network can effectively transmit the IMF features, the hidden layer can accurately fit the subsidence law, the loss function converges within a preset threshold, and the training of the BP neural network is completed.
[0073] Step 211: Using the trained BP neural network to perform future time series prediction on the plurality of IMF components, and superimposing the prediction results of each IMF component to obtain an overall ground subsidence prediction result.
[0074] Step 212: Comparing the overall ground subsidence prediction result with the actual observation data, and if the prediction performance does not meet the preset standard, adjusting the VMD decomposition parameters or the BP neural network parameters and re-executing the above steps until a prediction result that meets the preset standard is obtained.
[0075] In the embodiments of the present application, a validation set or a hold-out set independent of the above training samples is selected as an evaluation benchmark to evaluate the deviation between the overall land subsidence prediction sequence and the actual observation sequence of the corresponding period. Specifically, the prediction error RMSE, MAE, MAE, and other evaluation indicators between the overall land subsidence prediction sequence and the actual observation sequence are calculated, and the calculated RMSE, MAE, and MAPE are compared with the preset standard. The above-mentioned preset standard includes RMSE≤10mm, MAE≤8mm or MAPE≤15%. According to the comparison result, the VMD parameter or the BP neural network structure and hyperparameter are adjusted, and the decomposition, training and prediction are re-performed, and the above process is repeated until the evaluation indicators tend to be stable.
[0076] To evaluate the prediction effect of land subsidence, the present application selects LSTM, VMD-LSTM and the VMD-BP model provided by the present application for multi-model comparison experiments, as shown in Table 1. For the severe subsidence area (point A), the prediction error between the overall land subsidence prediction sequence and the actual observation sequence is calculated to obtain the evaluation indicators RMSE, MAE, and MAPE. The prediction error of the VMD-BP model on the test set is: RMSE is 0.28mm, MAE is 0.23mm. Compared with the VMD-LSTM model, the RMSE reduction rate is as high as 97.3%, and the MAE reduction rate is 97.6%, which fully reflects that the VMD-BP model has better prediction accuracy in this area.
[0077] Model Train set RMSE Train set MAE Train set MAPE Test set RMSE Test set MAE Test set MAPE LSTM 2.5846 2.146 13.52％ 13.6801 12.0246 20.12％ VMD-LSTM 1.4109 1.2687 7.50％ 10.5318 9.5863 16.26％ VMD-BP 0.0306 0.02289 0.12％ 0.27801 0.23429 0.39％
[0078] Compared with the prior art, the technical scheme provided by the second embodiment of the present application has the following beneficial effects:
[0079] The technical scheme of the present application uses SBAS-InSAR technology combined with geographic coding to accurately obtain the spatio-temporal distribution of regional-scale land subsidence. Through VMD decomposition, the subsidence time series signal is separated at multiple scales, and based on energy contribution degree, signal-to-noise ratio and other quantitative indicators, the effective components are screened, which can effectively eliminate noise interference, highlight the core features of subsidence and improve signal purity. Further, the BP neural network is used to predict the screened IMF components, and the sliding window sample structure, cross-validation parameter optimization, and early stopping / regularization are used to prevent overfitting, which significantly enhances the learning ability and prediction accuracy of the model for complex subsidence patterns. Through the RMSE, MAE and other indicators, a closed-loop feedback mechanism is constructed to dynamically adjust the VMD and neural network parameters, ensuring the adaptability and stability of the model in different scenarios.
[0080] While embodiments of the application have been shown and described, it is to be understood that the embodiments described are merely exemplary and that changes can be made in detail without departing from the principles and spirit of the application. The scope of the application is therefore defined by the appended claims and their equivalents.
Claims
1. A method for predicting land subsidence based on variational mode decomposition and BP neural network, characterized in that, include: Acquire multi-temporal SAR images of the area to be monitored; After performing topographic phase correction and atmospheric delay phase correction on the multi-temporal SAR images, an interferometric pair network is constructed using the small baseline set SBAS technique. After noise removal from the interferogram, screening of low coherence areas, and phase unwrapping, the acquired absolute phase is converted into surface subsidence and geocoded to obtain the spatiotemporal distribution of subsidence in the area to be monitored, so as to extract the original temporal signal of the surface subsidence monitoring point. VMD is used to perform multi-scale decomposition on the original time-series signal to obtain multiple intrinsic mode functions (IMFs). The target mode function is selected based on the energy contribution or signal-to-noise ratio of each IMF. The historical time series data of the selected target mode functions are used as input to the BP neural network. The BP neural network is trained and future time series predictions are made for each IMF component. The prediction results of each IMF component are superimposed to obtain the overall surface subsidence prediction result. The overall surface subsidence prediction results are compared with the actual observation data. If the prediction performance does not meet the preset standard, the VMD decomposition parameters or BP neural network parameters are adjusted and the above steps are repeated until a prediction result that meets the preset standard is obtained.
2. The land subsidence prediction method based on variational mode decomposition and BP neural network according to claim 1, characterized in that, After acquiring multi-temporal SAR images of the area to be monitored, the method further includes: The digital elevation model (DEM) data, atmospheric correction data, and satellite precise orbit data corresponding to the multi-temporal SAR image are acquired; wherein, the DEM data is used to perform terrain phase correction on the multi-temporal SAR image, and the satellite precise orbit data is used to correct the phase deviation caused by satellite orbit position error.
3. The land subsidence prediction method based on variational mode decomposition and BP neural network according to claim 1, characterized in that, An interferometric pair network is constructed using the small baseline set SBAS technique, including: Baseline estimation is performed on the corrected multi-temporal SAR image to determine the spatial and temporal baselines of the multi-temporal SAR image; Interferometric pairs are generated by filtering multi-temporal SAR images that meet the conditions according to a preset baseline threshold, forming the interferometric pair network; wherein, the baseline threshold includes a spatial baseline threshold and a temporal baseline threshold.
4. The land subsidence prediction method based on variational mode decomposition and BP neural network according to claim 1, characterized in that, After constructing the interferometric pair network using the small baseline set SBAS technique, the method further includes: Within the area to be monitored, a stable region is selected as a reference point, which is a region with high coherence and no significant deformation; Based on the aforementioned interference, the network is subjected to interferogram generation, noise removal, and phase unwrapping to obtain a continuous absolute phase; Based on the unwrapped absolute phase, the temporal phase changes of each monitoring point in the area to be monitored are extracted, and the temporal phase changes are converted into corresponding surface subsidence. After geocoding, the spatiotemporal distribution of subsidence in the area to be monitored is obtained.
5. The land subsidence prediction method based on variational mode decomposition and BP neural network according to claim 1, characterized in that, The original time-series signal is decomposed into multiple intrinsic mode functions (IMFs) using VMD at multiple scales, including: The original time-series signal is decomposed into multiple Integral Multi-Functions (IMFs) by constructing and solving an optimization objective function. The optimization objective function minimizes the bandwidth of each IMF and ensures that the sum of all IMFs equals the original time-series signal. This optimization objective function is obtained by iteratively updating each IMF and its corresponding center frequency, and is expressed as follows: In the formula, u k (t) is the k-th mode function, ω k It corresponds to the center frequency, and u is updated iteratively. k (t) and ω k The process yields the decomposed mode functions; The partial derivative with respect to time describes the rate of change of the signal; δ(t) represents the Dirac delta function; This represents the square of the L2 norm.
6. The land subsidence prediction method based on variational mode decomposition and BP neural network according to claim 1, characterized in that, The selected historical time-series data of the target mode function are used as input to the BP neural network to train the BP neural network, including: Training samples are constructed using a sliding window approach; the sample input consists of the N-step numerical combinations corresponding to the previous N steps in the historical time series of multiple IMF components, and the sample label consists of the numerical combinations of the current step or a future step in the time series corresponding to multiple IMF components.
7. The land subsidence prediction method based on variational mode decomposition and BP neural network according to claim 1, characterized in that, The overall surface subsidence prediction results are compared with actual observation data to determine whether the prediction performance meets the preset standards, including: Calculate the prediction errors RMSE, MAE, and MAPE between the overall surface subsidence prediction results and the actual observation results, and compare the prediction errors with preset standards; Based on the comparison results, adjust the VMD parameters or BP neural network structure and hyperparameters, re-decompose, train and predict, and repeat the above steps until the prediction error tends to stabilize.