Ground surface settlement monitoring method based on synthetic aperture radar image

Abstract

The invention discloses a ground surface settlement monitoring method based on synthetic aperture radar images, and relates to the technical field of ground surface deformation monitoring. Comprising the following steps: acquiring a real-time rail lifting value of a to-be-processed synthetic aperture radar image obtained by rail lifting imaging; inputting the real-time rail lifting value into the trained ridge regression model to obtain a real-time rail lifting fusion preliminary prediction value; carrying out modeling on a residual error generated by the trained ridge regression model in a prediction process through the trained autoregression integrated moving average model to obtain a real-time prediction residual error; and superposing the real-time lifting rail fusion preliminary prediction value and the real-time prediction residual error to obtain a real-time lifting rail fusion final prediction value, and using the real-time lifting rail fusion final prediction value to extract ground surface settlement deformation information. According to the method, the rail lifting fusion value can be obtained only by processing the rail lifting value, the dependency of traditional InSAR double-rail fusion is broken through, and a new normal form is provided for single-rail data deformation monitoring.

Description

Technical Field

[0001] The present invention relates to the technical field of surface deformation monitoring, and in particular to a surface subsidence monitoring method based on synthetic aperture radar images. Background Art

[0002] Interferometric Synthetic Aperture Radar (InSAR) is a technique for measuring surface elevation and deformation by analyzing the phase information of multiple synthetic aperture radar (SAR) images. The basic concept of InSAR is to use radar to obtain surface echo signals from different locations (or the same location at different times) and calculate the phase difference between these images to extract surface geometric characteristics, including topographic change and deformation monitoring.

[0003] Existing technology, D-InSAR (Differential InSAR) technology, enables surface subsidence monitoring by fusing ascending and descending data. The process is as follows: First, synthetic aperture radar images of the same area are acquired in ascending and descending directions. The two images are precisely registered to ensure that points of the same name correspond to the same ground resolution unit. Next, an interferogram of the ascending and descending data is generated. An external digital elevation model (DEM) is used to remove the terrain phase, and a filtering algorithm is used to suppress noise while preserving the deformation phase information. Because the ascending and descending data have different radar wave incidence angles, their sensitivities to surface deformation vary. Phase unwrapping and geocoding are used to convert the two data orbits to the same geographic coordinate system. The ascending and descending data are then fused to produce an ascending and descending fusion result that includes deformation information. Leveraging multi-view observations, phase unwrapping is performed on the ascending and descending orbit fusion results to compensate for monitoring blind spots caused by geometric distortion or loss of coherence in single-orbit data, reduce the effects of geometric distortions such as shadows and overlap, and generate line-of-sight deformation maps. Geocoding of these line-of-sight deformation maps enables millimeter-level surface subsidence monitoring and provides information on surface subsidence and deformation.

[0004] D-InSAR relies on the complementary nature of ascending and descending data. Ascending data provides one perspective, while descending data allows for observations from the other. The combination of the two effectively compensates for blind spots caused by geometric distortion or incoherence in single-orbit data. However, D-InSAR uses satellite data acquired by Sentinel satellites, which can only obtain ascending data over most areas, but not descending data. This means that the ascending data cannot be verified or supplemented, resulting in D-InSAR's inability to fully capture surface deformation information. This can lead to biases or omissions in monitoring results, compromising accurate assessments of surface deformation conditions. Summary of the Invention

[0005] Based on this, it is necessary to provide a surface subsidence monitoring method based on synthetic aperture radar images to address the above technical problems.

[0006] An embodiment of the present invention provides a surface subsidence monitoring method based on synthetic aperture radar images, comprising: Obtaining the real-time orbit raising value of the synthetic aperture radar image to be processed obtained by orbit raising imaging; The real-time ascending orbit value is input into the trained ridge regression model to obtain the real-time ascending and descending orbit fusion preliminary prediction value; The residuals generated by the trained ridge regression model during the prediction process are modeled using the trained autoregressive integrated moving average model to obtain real-time prediction residuals; The real-time ascending and descending orbit fusion preliminary prediction value and the real-time prediction residual are superimposed to obtain the real-time ascending and descending orbit fusion final prediction value, which is then used to extract surface settlement and deformation information.

[0007] Optionally, training the ridge regression model specifically includes: Acquire multiple historical synthetic aperture radar images including historical ascending and descending values, fuse them using small baseline set interferometric synthetic aperture radar technology to obtain the true ascending and descending fusion values; The historical ascending orbit values ​​of historical synthetic aperture radar images are input into the ridge regression model to obtain the ascending orbit fusion prediction value. The ridge regression model is trained with the goal of minimizing the deviation between the ascending orbit fusion prediction value and the ascending orbit fusion true value to obtain the trained ridge regression model.

[0008] Optionally, the historical ascending orbit values ​​and the historical descending orbit values ​​on multiple historical synthetic aperture radar images are fused using a small baseline set interferometric synthetic aperture radar technology based on the following formula to obtain the ascending and descending orbit fusion true value: ; Where, is the incident angle of the ascending SAR, is the SAR incidence angle for descending orbit, is the flight azimuth of the ascending SAR, is the azimuth of the descending SAR flight, is the observation value of the deformation along the line of sight of the ascending InSAR, is the line-of-sight deformation observation value of the descending InSAR.

[0009] Alternatively, the historical ascending orbit values ​​can be input into the ridge regression model based on the following formula to obtain the ascending and descending orbit fusion prediction value: in, is the historical rising track value, is the ascending and descending orbit fusion prediction value, is the intercept term, is the slope term.

[0010] Optionally, the real-time ascending orbit value of the synthetic aperture radar image to be processed is input into the trained ridge regression model to obtain a preliminary prediction value of the real-time ascending and descending orbit fusion, specifically including: The trained ridge regression model is obtained by ， Perform linear mapping on the real-time orbit raising value and obtain the preliminary prediction value of the real-time orbit raising and lowering fusion based on the following formula: ; in, It is the preliminary prediction value of real-time ascending and descending orbit fusion, It is the real-time track ascending value.

[0011] Optionally, training the autoregressive integrated moving average model specifically includes: Perform a stationary test on the residual sequence and eliminate non-stationarity by d; Determine q based on the autocorrelation function and determine p based on the partial autocorrelation function; According to the preliminarily determined p, d, and q, multiple candidate autoregressive integrated moving average models are fitted; the multiple autoregressive integrated moving average models are compared using the information criterion, and the autoregressive integrated moving average model with the lowest information value is selected as the final autoregressive integrated moving average model; Where d is the number of differences, q is the moving average order, and p is the autoregressive order.

[0012] The surface subsidence monitoring method based on synthetic aperture radar images provided by the embodiment of the present invention has the following beneficial effects compared with the prior art: To address the problem of missing descending orbit data, the present invention combines the ridge regression model with the autoregressive integrated moving average model. The ascending and descending orbit fusion values ​​can be obtained by processing only the ascending orbit values. This breaks through the dependence of traditional InSAR dual-orbit fusion and provides a new paradigm for deformation monitoring using single-orbit data. It is particularly suitable for areas where descending orbit data are missing, such as basin boundaries, mining area surfaces, polar regions, and mountainous areas. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 A schematic diagram of a D-InSAR differential interferometry measurement principle of a surface subsidence monitoring method based on synthetic aperture radar images provided in one embodiment; Figure 2 A conventional differential interferometry deformation monitoring flow chart of a surface subsidence monitoring method based on synthetic aperture radar images provided in one embodiment; Figure 3 SBAS-InSAR data processing flow chart of a surface subsidence monitoring method based on synthetic aperture radar images provided in one embodiment; Figure 4 is an SBAS-InSAR surface subsidence rate map of a surface subsidence monitoring method based on synthetic aperture radar images provided in one embodiment, Figure 4 (a) is the surface sedimentation rate map of the ascending orbit SBAS-InSAR. Figure 4 (b) is the descending SBAS-InSAR surface subsidence rate map; Figure 5 The following is a subsidence rate result of SBAS-InSAR ascending and descending track fusion of a surface subsidence monitoring method based on synthetic aperture radar imagery provided in one embodiment; Figure 6 This is a comparison diagram of the subsidence results of SBAS-InSAR observation lines of a surface subsidence monitoring method based on synthetic aperture radar images provided in one embodiment. Figure 6 (a) is a comparison chart of the dip line sinking results. Figure 6 (b) is a comparison chart of the sinking results of the strike line; Figure 7 FIG. 1 is a diagram showing the SBAS-InSAR interpolation result of a surface subsidence monitoring method based on synthetic aperture radar images provided in one embodiment. Figure 7 (a) is the result after ascending orbit interpolation. Figure 7 (b) is the result after descending orbit interpolation; Figure 8 A comparison diagram of simulated subsidence basins in a surface subsidence monitoring method based on synthetic aperture radar images provided in one embodiment. Figure 8 (a) is a simulated ascending and descending track fusion sinking basin map. Figure 8(b) is the actual ascending and descending track fused sinking basin map; Figure 9 A comparison diagram of the trend lines of simulation results and actual results of a surface subsidence monitoring method based on synthetic aperture radar images provided in one embodiment; Figure 10 A comparison diagram of the simulation results and actual observation lines of a surface subsidence monitoring method based on synthetic aperture radar images provided in one embodiment; Figure 11 A simulated subsidence basin map of an ascending and descending track fusion method of a surface subsidence monitoring method based on synthetic aperture radar images provided in one embodiment; Figure 12 This is a comparison diagram of the subsidence results of the simulated ascending and descending track fusion observation line of a surface subsidence monitoring method based on synthetic aperture radar images provided in one embodiment. Figure 12 (a) is a comparison chart of the dip line sinking results. Figure 12 (b) is a comparison chart of the sinking results of the strike line; Figure 13 The figure is a flow chart of a surface subsidence monitoring method based on synthetic aperture radar images provided in one embodiment. DETAILED DESCRIPTION

[0014] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0015] The embodiment of the present invention provides a surface subsidence monitoring method based on synthetic aperture radar images, such as Figure 13 As shown, the method includes: Obtaining the real-time orbit raising value of the synthetic aperture radar image to be processed obtained by orbit raising imaging; The real-time ascending orbit value is input into the trained ridge regression model to obtain the real-time ascending and descending orbit fusion preliminary prediction value; The residuals generated by the trained ridge regression model during the prediction process are modeled using the trained autoregressive integrated moving average model to obtain real-time prediction residuals; The real-time ascending and descending orbit fusion preliminary prediction value and the real-time prediction residual are superimposed to obtain the real-time ascending and descending orbit fusion final prediction value, which is then used to extract surface settlement and deformation information.

[0016] The training of the ridge regression model specifically includes: Multiple historical synthetic aperture radar images including historical ascending orbit values ​​and historical descending orbit values ​​are obtained, and the historical ascending orbit values ​​and historical descending orbit values ​​are fused using the small baseline set interferometric synthetic aperture radar technology to obtain the true ascending and descending orbit fusion values.

[0017] The historical ascending orbit values ​​of historical synthetic aperture radar images are input into the ridge regression model to obtain the ascending orbit fusion prediction value. The ridge regression model is trained with the goal of minimizing the deviation between the ascending orbit fusion prediction value and the ascending orbit fusion true value to obtain the trained ridge regression model.

[0018] The training of the autoregressive integrated moving average model specifically includes: The residual series is tested for stationarity and non-stationarity is eliminated by d.

[0019] q is determined from the autocorrelation function, and p is determined from the partial autocorrelation function.

[0020] Based on the preliminarily determined values ​​of p, d, and q, multiple candidate autoregressive integrated moving average models are fitted. The information criterion is used to compare these models, and the one with the lowest information value is selected as the final autoregressive integrated moving average model. Here, d is the number of differencing steps, q is the moving average order, and p is the autoregressive order.

[0021] Specific implementation includes: 1. Traditional single-track InSAR principle.

[0022] InSAR is a technology that measures surface height and deformation by analyzing the phase information of multiple SAR images. The basic concept of InSAR is to use radar to acquire surface echo signals from different locations (or the same location at different times) and calculate the phase difference between these images to extract geometric changes in the surface, including topographic changes and deformation monitoring.

[0023] D-InSAR extracts surface deformation information by performing differential processing on two SAR images taken at different times, eliminating the terrain phase. The basic principle is to use SAR images acquired using a three- or two-track method, calculate the phase difference in the interferogram, and then obtain deformation information after removing the terrain effect.

[0024] The basic principle and processing flow of synthetic aperture radar differential interferometry are explained using the "two-track" method D-InSAR as an example. Figure 1 shown.

[0025] Figure 1In the equation ( ), A1 and A2 refer to the spatial positions of the satellite when it images the same area twice; R1 and R2 represent the distances between the satellite and a specific ground target P at these two time points; H represents the vertical height of the satellite relative to the ground at the time of the first imaging; h represents the deformation of the ground target during the two imaging processes, that is, the displacement from the initial position P to the deformed position P'; B is the distance moved by the radar satellite sensor during the two imaging processes, which is the spatial baseline; the spatial baseline B can be further decomposed into two components: the component B⊥ perpendicular to the radar line of sight, and the component B∥ parallel to the radar line of sight; α is the azimuth, which is the angle between the spatial baseline B and the horizontal plane, and θ is the angle of incidence, which is the angle between the radar line of sight and the ground normal.

[0026] (1) In the case of repeated orbit interferometry, the InSAR interferometry phase is related to factors such as the selected reference ellipsoid, the location of the ground point, whether the ground surface is deformed and the extent of the deformation, atmospheric delay error, and SAR system noise. The interferometric phase can be expressed as follows:

[0027] (2) Where: is the reference ellipsoid phase; is the terrain phase; is the deformation phase along the line of sight (LOS); is the phase caused by orbit error; is the atmospheric delay phase; is the phase caused by noise.

[0028] To obtain the deformation phase along the line of sight (LOS) , then it is necessary to remove the reference ellipsoid phase , terrain phase , phase caused by orbit error Phase delay with atmosphere .

[0029] like Located on the reference ellipsoid (i.e., the elevation relative to the reference ellipsoid is zero), its contribution to the interference phase is called .like Figure 1 As shown, 、 Target points The distance to the two positions of the radar antenna is , so it can be approximately considered that and Parallel, so the target point interference phase It can be expressed as:

[0030] (3) If the target point If the point is located on complex terrain and not on the reference ellipsoid, the interference phase of the point includes both the terrain phase and the reference ellipsoid phase. Figure 1 As shown, since the target point and To the satellite dish location If the distances are equal, Point and reference ellipsoid Correspondingly, the viewing angle changes after the point moves , 、 for The distance to the two satellites can be obtained from the geometric relationship The interference phase of the point is:

[0031] (4) Therefore, the terrain phase It can be expressed as: (5) Depending on the radar's height above the ground, the incident angle will change from short distance to long distance, thus affecting the imaging geometry. The relationship between them is as follows:

[0032] (6) (7) For the phase caused by orbit error Phase delay with atmosphere First, we use precise orbit data to perform preliminary orbit error correction. We then combine this with an atmospheric correction model to remove atmospheric errors. Finally, we use the reference point method to further reduce the remaining orbit and atmospheric errors. Therefore, without considering the effects of atmospheric and noise phases, we can assume that the interferometric phase is primarily composed of terrain phase, reference ellipsoid phase, and surface deformation phase. Using the above formula, we can calculate the LOS deformation phase.

[0033] (8) Therefore, the LOS deformation obtained by D-InSAR differential interferometry is The expression can be expressed as (9) The conventional D-InSAR differential interferometry measurement process is as follows: Figure 2 .

[0034] The basic principle of Small Baseline Subset InSAR (SBAS-InSAR) is to use the deformation results obtained by a single conventional D-InSAR as observations and then obtain a high-precision deformation time series based on the least squares principle. Its processing flow mainly includes the generation of differential interferograms, the selection of point targets, the unwrapping of differential interferograms, and the acquisition of time deformation series. Figure 3 As shown; from Figure 2~Figure 3 It can be seen that the deformation calculated by InSAR is all along the LOS direction. The LOS vector is the direction in which the radar signal contacts the surface, and the deformation of the surface can be divided into three components: north-south, east-west, and vertical. In this decomposition process, assuming that the radar detects the deformation of a certain point in the LOS direction, combined with the horizontal and vertical displacements of the point, we can use the formula to decompose the LOS vector into the corresponding displacement components in the east-west, north-south, and vertical directions. The specific formula is:

[0035] (10) In practical applications, single-track InSAR technology can only detect displacement in the radar's line of sight (i.e., deformation in the LOS direction), and cannot separate specific displacement information in the east-west and vertical directions. Existing InSAR monitoring methods simply ignore east-west and north-south horizontal movement to estimate subsidence. Thus, the formula for calculating surface subsidence is:

[0036] (11) 2. The principle of InSAR fusion of ascending and descending orbits.

[0037] Traditional single-track InSAR estimates of subsidence simply ignore east-west and north-south horizontal movement. However, the mining area has experienced significant surface subsidence, and simply ignoring these east-west and north-south horizontal movement makes estimates of subsidence inaccurate.

[0038] By fusing ascending and descending orbits, and leveraging the complementarity of data from ascending and descending orbits, we can observe surface deformation from different angles, overcoming the limitations of a single orbit. This ascending and descending InSAR technique only ignores minor north-south deformation, allowing for more precise separation of vertical surface deformation.

[0039] (12) Where, is the incident angle of the ascending SAR, is the SAR incidence angle for descending orbit, is the flight azimuth of the ascending SAR, is the azimuth of the descending SAR flight, is the observation value of the deformation along the line of sight of the ascending InSAR, is the line-of-sight deformation observation value of the descending InSAR.

[0040] 3. Comparison of single-track and ascending-orbit fusion InSAR solution results.

[0041] Taking the surface monitoring data of the 150202 working face in Ningdong mining area as an example, the single-track and ascending-orbit fusion SBAS-InSAR solution is performed. Figure 4 The results are shown and compared with the actual leveling results.

[0042] Overall, the subsidence basin is located above the mined working face, which conforms to the general law of mining subsidence, but there are still great differences in the specific details. In fact, this is caused by the peak-valley error pattern (i.e., overestimation and underestimation errors) of the single-track image monitoring method. When imaging in the ascending orbit, the subsidence on the west and east sides of the basin is overestimated and underestimated respectively, resulting in the expansion of the western boundary and the rapid convergence of the eastern boundary; while in the descending orbit imaging, a movement and contraction phenomenon similar to that of the ascending orbit but in the opposite direction occurs, with the western boundary of the basin converging rapidly and the eastern boundary expanding. This is mainly because the perspectives of the ascending and descending orbits are different, resulting in different geometric relationships in the observation directions. The projection of the surface deformation in the ascending and descending orbit line of sight will be different. This projection difference may lead to deviations in the deformation results. In addition, atmospheric effects, orbit errors, terrain undulations, and differences in time and space baselines will also introduce errors. These factors jointly affect the consistency of the ascending and descending orbit results, especially in areas with complex terrain or significant nonlinear deformation. After the ascending and descending orbit fusion, the images caused by the above factors can be reduced and more accurate results can be obtained. Figure 5 shown.

[0043] In order to more accurately obtain the micro-deformation monitoring accuracy of ascending and descending SBAS-InSAR and conventional SBAS-InSAR, and to qualitatively and quantitatively verify the improvement of the deformation monitoring accuracy of SBAS-InSAR technology by ascending and descending fusion technology, the actual measured leveling data of 30 points with small deformation magnitude, including two control points R1 and R2 on the inclination line and 17 monitoring points Q1-Q17, and three control points R5, R6, and R7 on the strike line and 8 monitoring points Z1-Z8, are selected to compare the ascending and descending results, as well as the ascending and descending fusion results. Figure 6 shown.

[0044] Table 1 SBAS-InSAR data accuracy statistics As shown in Table 1, the root mean square errors of ascending SBAS-InSAR, descending SBAS-InSAR, and ascending-and-descending SBAS-InSAR fusion are 29.42 mm, 24.84 mm, and 5.56 mm, respectively. Compared to single-track SBAS-InSAR, the use of fused ascending-and-descending technology improves monitoring accuracy by 77%. Experimental results demonstrate that the use of fused ascending-and-descending SBAS-InSAR technology achieves millimeter-level monitoring accuracy, enabling the demarcation of subsidence basins and better monitoring of small-gradient surface deformation in mining areas.

[0045] 4. Predict ascending and descending orbit fusion based on the Ridge Regression model and the Autoregressive Integrated Moving Average Model (ARIMA).

[0046] Based on the above analysis, we conclude that ascending-orbit fusion InSAR technology can significantly improve the accuracy of mining area subsidence monitoring. In particular, ascending-orbit fusion SBAS-InSAR technology can achieve millimeter-level accuracy, meeting the needs of monitoring small-gradient surface deformation in mining areas. However, due to the lack of descending satellite imagery from Sentinel-1 in many areas, a technical framework for simulating ascending-orbit fusion results based on a ridge regression model and an autoregressive integrated moving average model is proposed. This method effectively improves the accuracy and stability of the simulated ascending-orbit results by preprocessing the ascending and fused data, performing feature engineering, modeling, and correction.

[0047] 4.1 Principles related to ridge regression model and ARIMA.

[0048] 4.1.1 Principle of ridge regression model.

[0049] Ridge regression, also known as Tikhonov regularization, is a linear regression method that addresses multicollinearity by introducing L2 regularization. Traditional linear regression models estimate regression coefficients by minimizing the sum of squared residuals. However, when there is linear dependence or high correlation between independent variables, ordinary least squares (OLS) regression can easily lead to unstable regression coefficients, which in turn can cause model overfitting. Ridge regression, by adding an L2 norm penalty term to the least squares loss function, aims to improve the model's generalization ability by controlling the size of the regression coefficients. This is particularly effective when there are many highly correlated features.

[0050] The optimization goal of ridge regression is to minimize the following loss function: (13) in, It is The actual observed value of the sample, It is The feature vector of the samples, is the regression coefficient vector, is the regularization parameter that controls the constraint strength of the regression coefficient. is the residual sum of squares in the least squares method, which is used to measure the degree of fit of the model; the second The L2 regularization term penalizes the sum of squares of the regression coefficients, limiting their size and preventing overfitting. This regularization term ensures that the regression coefficients are not too large, making the model more stable and having better generalization performance.

[0051] By adjusting the regularization parameter , a balance can be found between fitting error and model complexity. When the value of is large, the influence of the regularization term on the loss function increases, and the regression coefficient tends to zero, making the model more concise; on the contrary, when When is small, the influence of the regularization term is reduced, ridge regression approaches ordinary least squares regression, and the regression coefficients can better fit the data. Therefore, ridge regression controls the complexity of the model by "penalizing" the regression coefficients, thereby improving the stability of the model. Especially when there is multicollinearity between processing features or when the data dimension is high, ridge regression can effectively avoid extreme fluctuations in the coefficients and is more robust to noise.

[0052] The closed-form solution of the ridge regression model can be obtained by the following formula: (14) in, is the design matrix, is the identity matrix, is the regularization parameter, is the observation vector. Using this formula, ridge regression can effectively solve for regression coefficients in high-dimensional data, thus avoiding the computational difficulties and instability of ordinary least squares when the number of features is large. Overall, ridge regression is a powerful regression method that can handle multicollinearity and overfitting, making it particularly suitable for modeling and analyzing high-dimensional data.

[0053] Input the historical ascending orbit value into the ridge regression model to obtain the ascending and descending orbit fusion prediction value: in, It is the historical rising track value; is the fusion prediction value of ascending and descending orbits; is the intercept term, which represents the reference offset of the ascending and descending orbit fusion value when the historical ascending orbit value is zero; is the slope term, which represents the expected change in the ascending and descending orbit fusion value when the historical ascending orbit value increases by one unit.

[0054] 4.1.2 ARIMA principle.

[0055] ARIMA consists of three main components: autoregressive (AR), integrated (I), and moving average (MA). Its mathematical expression is ARIMA(p, d, q), where p, d, and q represent the order of the AR term, the number of differencing, and the order of the MA term, respectively.

[0056] The autoregressive (AR) part describes the relationship between the current value and its values ​​at the past p moments. Specifically, the current value is a linear combination of the past p values, plus a random error term. The mathematical expression is:

[0057] (15) Where, are model parameters, is the white noise error term.

[0058] Difference (I) part: used to convert non-stationary time series data into a stationary series. By performing d-order difference on the data, that is, performing d-time difference operations continuously, the trend and seasonal components are eliminated. The expression of the first-order difference is:

[0059] (16) The second-order difference is: (17) Moving Average (MA): describes the relationship between the current value and the error term at the past q moments. The current value depends not only on the past value, but also on the random errors at the past q moments. The mathematical expression is:

[0060] (18) Where, are model parameters, is the white noise error term.

[0061] In summary, the ARIMA model, by combining AR, I, and MA, can effectively capture the autocorrelation, trend, and random fluctuations in time series data, providing a basis for subsequent predictions.

[0062] The effectiveness of the ARIMA model depends on the accurate selection of its three parameters p, d, and q. Parameter identification usually involves the following steps:

[0063] Data Stationarity Test: Before fitting an ARIMA model, you need to confirm the stationarity of the time series data. Common methods include plotting a time series graph, calculating the autocorrelation function (ACF) and partial autocorrelation function (PACF), and performing unit root tests (such as the Augmented Dickey-Fuller test or ADF test). If the data is non-stationary, differencing is necessary to make it stationary.

[0064] Determine the number of differencing steps, d: By observing the time series plot and performing a unit root test, determine how many orders of differencing are needed to make the series stationary. Typically, start with the first order of differencing and gradually increase the number of differencing steps until the series exhibits stationary behavior.

[0065] Determine the autoregressive order p: This is determined by observing the PACF plot. If the PACF plot shows significant truncation at lag k, p = k is usually chosen.

[0066] Determine the moving average order q by observing the ACF plot. If the ACF plot shows significant truncation at lag k, q = k is usually selected.

[0067] Model Fitting and Diagnostics: Fit the ARIMA model based on the preliminarily determined p, d, and q parameters. Evaluate the model fit by examining the autocorrelation of the residuals (e.g., using the Ljung-Box test) and normality (e.g., using a QQ plot). If the residuals exhibit autocorrelation or deviate from a normal distribution, re-adjust the model parameters.

[0068] Model selection criteria: Among multiple candidate models, information criteria (such as Akaike Information Criterion, AIC; Bayesian Information Criterion, BIC) are used for comparison, and the model with the lowest AIC or BIC value is selected as the final model.

[0069] 4.1.3 Combination of Ridge Regression and ARIMA Models.

[0070] First, multiple historical synthetic aperture radar (SAR) images are acquired. The historical ascending and descending values ​​from these images are fused using small baseline set interferometric SAR (ISAR) technology to obtain the true ascending and descending values. Ridge regression is then used to predict the historical ascending values ​​based on the historical SAR images.

[0071] Ridge regression avoids overfitting in the regression process by introducing a regularization term, resulting in a fusion prediction of the ascending and descending orbits. The ridge regression model is trained with the goal of minimizing the deviation between the fusion prediction and the true value of the ascending and descending orbits, resulting in a trained ridge regression model.

[0072] After the ridge regression model is trained, the regression error is calculated by calculating the residuals between the true and predicted values. These residuals may contain information about the autocorrelation in the time series, which the ridge regression model alone does not fully capture. Therefore, the ARIMA model is then applied to these residuals for modeling.

[0073] The ARIMA model models the residuals by learning the temporal characteristics of the residual sequence (such as autocorrelation) and uses this model to predict future residuals, generating predicted residuals. By adding the predicted residuals from the ARIMA model to the initial predictions of the ascending and descending orbit fusion from ridge regression, a more accurate final prediction of the ascending and descending orbit fusion is obtained. This correction process effectively improves the prediction accuracy of ascending orbit data, especially when dealing with regression problems with complex time series patterns, and can better capture the inherent laws of the data.

[0074] By combining ridge regression with the ARIMA model, we can not only deal with the problem of multicollinearity, but also optimize the residual performance of the model through time series analysis, thereby obtaining more accurate simulation results of ascending and descending orbit fusion.

[0075] 4.2 Prediction of ascending and descending orbit fusion results.

[0076] Figure 3 From the surface subsidence rate of the ascending orbit and the surface subsidence rate of the ascending orbit fusion, it can be seen that there are a certain degree of null values ​​in both the ascending orbit result and the ascending orbit fusion result. This is because when the surface deformation exceeds a certain threshold, the interference phase difference is too large, which makes it impossible to accurately resolve the whole-cycle ambiguity, resulting in the data being unable to be reliably inverted. In addition, since the null values ​​of the ascending orbit result and the ascending orbit fusion result do not completely overlap, it is impossible to extract the checkpoint coordinates, which in turn makes it impossible to evaluate the accuracy of the sinking basin. In order to better predict the data, the ascending orbit result and the ascending orbit fusion result are kriging interpolated to obtain a complete sinking basin, as shown in the figure. Figure 7 shown.

[0077] After obtaining a complete picture of the subsidence basin, we first extracted and merged ascending and fused data from two different datasets. The original datasets contained ascending and fused values, each of which contained spatial location information and trajectory data associated with a specific time point. Next, by merging the data from different time points, we obtained a final dataset containing both ascending and fused values. To further enhance the model's fitting capabilities, we applied lag features and rolling statistics to the ascending data, improving the model's ability to capture temporal features. Based on these features, we constructed a ridge regression model.

[0078] During the model training phase, the twelve orbit-raising and sinking results (from December 2020 to May 7, 2021) and the sinking results of the fusion of orbit-raising and orbit-sinking were used as the training set for ridge regression fitting. Training was performed using the lagged characteristics and rolling statistical features of the orbit-raising values ​​as input, and the fusion values ​​as output. Through training of the ridge regression model, a set of regression coefficients was obtained, which were used to predict the training data. The residuals between the model's predicted values ​​and the true values ​​were calculated to evaluate the model's fit and provide a basis for subsequent residual correction. The regularization term in ridge regression effectively controls the complexity of the model and avoids overfitting. After model training, predictions were made on the training and test sets, and multiple evaluation metrics, such as mean squared error (MSE), coefficient of determination (R²), and mean absolute error (MAE), were calculated to evaluate the model's predictive performance.

[0079] Because the ridge regression model is a variant of linear regression, it may not fully capture the time series characteristics of the data. Therefore, to further improve the model's predictive accuracy, the residuals of the ridge regression model are introduced into time series analysis and the ARIMA model is used to model and correct the residuals. By capturing the autocorrelation in the time series, the ARIMA model effectively fits the residual distribution, thereby improving the accuracy of the final forecast results.

[0080] Finally, based on the combination of the ridge regression model and the ARIMA model, the trained ridge regression model is used to make a preliminary prediction of the real-time ascending orbit value, resulting in a preliminary prediction of the real-time ascending orbit fusion. Next, the residuals are modeled using the ARIMA model on the training set to obtain the real-time prediction residuals. These two results are added together to obtain the final prediction of the real-time ascending orbit fusion.

[0081] The trained ridge regression model is obtained by ， Perform linear mapping on the real-time orbit raising value and obtain the preliminary prediction value of the real-time orbit raising and lowering fusion based on the following formula: ; in, It is the preliminary prediction value of real-time ascending and descending orbit fusion, It is the real-time track-raising value; The real-time prediction residual and the real-time ascending and descending orbit fusion preliminary prediction value are superimposed to obtain the ascending and descending orbit fusion final prediction value: ; in, To predict the residual in real time, The preliminary prediction value is integrated into the real-time ascending and descending orbit.

[0082] The key to this process is to combine traditional regression methods with time series analysis methods to fully utilize the temporal and spatial characteristics of the data, thereby achieving accurate fusion of simulated ascending and descending orbits. The simulated ascending and descending orbit fusion sinking basin results on May 19, 2021 and the actual ascending and descending orbit fusion sinking basin results are as follows: Figure 8 shown.

[0083] 4.3 Prediction model accuracy assessment.

[0084] Depend on Figure 8 It can be seen that the overall trend of the simulated ascending and descending orbit fusion sinking basin is basically consistent with the actual sinking basin, and the overall basin range is also consistent. In order to quantitatively verify the reliability of the simulation results, the simulated sinking values ​​extracted from the ground observation station are compared with the actual sinking values ​​to determine the accuracy of the simulation results.

[0085] Depend on Figure 9 and Figure 10 It can be seen that the simulated ascending and descending orbit fusion results are basically the same as the actual ascending and descending orbit fusion results. The calculation of the errors of all points shows that the maximum error of the simulation results is 10.64mm, the average error is 1.64mm, and the root mean square error is 5.89mm. Combined with the calculation results, it can be seen that the simulation results are very good and can simulate the ascending and descending orbit fusion results very well. However, the accuracy of the simulation results of the sinking basin after the final stabilization still needs to compare the sinking basin results of the last phase on July 25, 2022 with the leveling measurement results of the surface observation station for accuracy analysis. The last phase of the simulated sinking basin is as follows Figure 11 shown.

[0086] according to Figure 11 It can be seen that the simulated ascending and descending track fusion results, corrected based on the ascending and descending results, are very good, with the basin center completely coinciding with the 150202 working surface. To quantitatively verify the accuracy of the simulated ascending and descending track fusion results, the simulation results were compared with the subsidence values ​​measured at the surface observation station. The accuracy analysis was performed using two control points R1 and R2 on the dip line and 12 monitoring points Q1-Q12, as well as three control points R5, R6, and R7 on the strike line and eight monitoring points Z1-Z8.

[0087] Table 2 Accuracy statistics of simulated ascending and descending orbit fusion data according to Figure 12 As shown in Table 2, the root mean square errors (RMS) of the ascending SBAS-InSAR and the simulated ascending-and-falling fusion SBAS-InSAR are 30.39 mm and 7.40 mm, respectively. Compared to the SBAS-InSAR results using ascending data alone, the accuracy of the simulated ascending-and-falling fusion SBAS-InSAR results is significantly improved. While not as accurate as the SBAS-InSAR results obtained using actual ascending-and-falling data in 3.4, the 7.40 mm RMS error is less than the 10 mm error of the subsidence basin boundary, allowing for clear demarcation of the subsidence basin boundary and meeting the requirements for small-gradient deformation monitoring in mining areas.

[0088] 5. Conclusion

[0089] To address the problem that single-track InSAR technology directly ignores east-west and north-south horizontal movement when estimating subsidence, thereby reducing monitoring accuracy and reliability, ascending and descending fusion is used to improve monitoring accuracy. Using the 130202 working face of the Yangchangwan Coal Mine as an example, ascending and descending SBAS-InSAR fusion was performed and its accuracy was verified by combining it with leveling data from surface observation stations. Compared to single-track SBAS-InSAR technology, accuracy improved by 77.0%, demonstrating the feasibility of fusion with ascending and descending InSAR for monitoring small-gradient surface subsidence. To address the issue of partially missing descending data, ridge regression and the ARIMIA model were proposed to fit the existing ascending and descending data, predicting the corrected ascending results to simulate the ascending and descending fusion results. The detection accuracy was 7.40 mm, meeting the requirements for monitoring small-gradient deformation in mining areas.

[0090] The above-described embodiments merely illustrate several implementations of the present invention. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, and all such variations and improvements fall within the scope of protection of the present invention.

Claims

1. A surface subsidence monitoring method based on synthetic aperture radar images, characterized in that: include: Obtaining the real-time orbit raising value of the synthetic aperture radar image to be processed obtained by orbit raising imaging; The real-time ascending orbit value is input into the trained ridge regression model to obtain the real-time ascending and descending orbit fusion preliminary prediction value; The residuals generated by the trained ridge regression model during the prediction process are modeled using the trained autoregressive integrated moving average model to obtain real-time prediction residuals; The real-time ascending and descending orbit fusion preliminary prediction value and the real-time prediction residual are superimposed to obtain the real-time ascending and descending orbit fusion final prediction value, which is then used to extract surface settlement and deformation information.

2. The method for monitoring ground subsidence based on synthetic aperture radar images according to claim 1, wherein: Training the ridge regression model specifically includes: Acquire multiple historical synthetic aperture radar images including historical ascending and descending values, fuse them using small baseline set interferometric synthetic aperture radar technology to obtain the true ascending and descending fusion values; The historical ascending orbit values ​​of historical synthetic aperture radar images are input into the ridge regression model to obtain the ascending orbit fusion prediction value. The ridge regression model is trained with the goal of minimizing the deviation between the ascending orbit fusion prediction value and the ascending orbit fusion true value to obtain the trained ridge regression model.

3. The surface subsidence monitoring method based on synthetic aperture radar images according to claim 2, characterized in that: Based on the following formula, the historical ascending and descending orbit values ​​on multiple historical synthetic aperture radar images are fused using the small baseline set interferometric synthetic aperture radar technology to obtain the true ascending and descending orbit fusion value: ； Where, is the incident angle of the ascending SAR, is the SAR incidence angle for descending orbit, is the flight azimuth of the ascending SAR, is the azimuth of the descending SAR flight, is the observation value of the deformation along the line of sight of the ascending InSAR, is the line-of-sight deformation observation value of the descending InSAR.

4. The method for monitoring ground subsidence based on synthetic aperture radar images according to claim 2, wherein: The historical ascending orbit values ​​are input into the ridge regression model based on the following formula to obtain the ascending and descending orbit fusion prediction value: ； in, is the historical rising track value, is the ascending and descending orbit fusion prediction value, is the intercept term, is the slope term.

5. The method for monitoring ground subsidence based on synthetic aperture radar images according to claim 4, characterized in that: The real-time ascending orbit value of the synthetic aperture radar image to be processed is input into the trained ridge regression model to obtain the real-time ascending orbit fusion preliminary prediction value, specifically including: The trained ridge regression model is obtained by ， Perform linear mapping on the real-time orbit raising value and obtain the preliminary prediction value of the real-time orbit raising and lowering fusion based on the following formula: ； in, It is the preliminary prediction value of real-time ascending and descending orbit fusion, It is the real-time track ascending value.

6. The method for monitoring ground subsidence based on synthetic aperture radar images according to claim 1, wherein: Training the autoregressive integrated moving average model specifically includes: Perform a stationary test on the residual sequence and eliminate non-stationarity by d; Determine q based on the autocorrelation function and determine p based on the partial autocorrelation function; According to the preliminarily determined p, d, and q, multiple candidate autoregressive integrated moving average models are fitted; the multiple autoregressive integrated moving average models are compared using the information criterion, and the autoregressive integrated moving average model with the lowest information value is selected as the final autoregressive integrated moving average model; Where d is the number of differences, q is the moving average order, and p is the autoregressive order.

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